2014
6
2
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A Mathematical Formulation to Estimate the Fundamental Period of HighRise Buildings Including FlexuralShear Behavior and Structural Interaction
2
2
The objective of the current study is to develop a simple formula to estimate the fundamental vibration period of tall buildings for using in equivalent lateral force analysis specified in building codes. The method based on SturmLiouville differential equation is presented here for estimating the fundamental period of natural vibration. The resulting equation, based on the continuum representation of tall buildings with various lateral resisting systems for natural vibration of the buildings, is proved to be the forthorder SturmLiouville differential equation, and a quick method for determining the fundamental period of natural vibration of the building is presented. Making use of the coupled wall theory for natural vibration, the method is extended to deal with vibration problem of other buildings braced by frame, walls or/and tube. The proposed formulation will allow a more consistent and accurate use of code formulae for calculating the earthquakeinduced maximum base shear in a building. Use of the method is economical with respect to both computer time and equipment and can be used to verify the results of the finite element analyses where the timeconsuming procedure of handling all the data can always be a source of errors.
1

122
134


E
Noroozinejad Farsangi
Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology, Tehran
Structural Engineering Research Center, Internatio
Iran
ehsan.noroozinejad@gmail.com


H
Melatdoust
Multimedia University, Cyberjaya, Malaysia
Multimedia University, Cyberjaya, Malaysia
Iran


A
Bin Adnan
Civil Engineering Department, University of Technology Malaysia, Johor Bahru, Malaysia
Civil Engineering Department, University
Iran
Fundamental period
continuum
FEA
4th order sturmliouville differential equation
[[1] Goel R. K., Chopra A. K., 1997, Period formulas for moment resisting frame buildings, Journal of Structural Engineering 123(11):14541461.##[2] Goel R. K., Chopra A. K., 1998, Period formulas for concrete shear wall buildings, Journal of Structural Engineering 124(4):426433.##[3] Heidebrecht A. C., Smith S. S., 1973, Approximate analysis of tall wallframe structures, Journal of the Structural Division 99(2):199221.##[4] Smith B. S., Yoon Y. S., 1991, Estimating seismic base shears of tall wallframe buildings, Journal of Structural Engineering 117(10):30263041.##[5] Wallace J.W., 1995, Seismic design of RC structural walls, Part I: New code format, Journal of Structural Engineering 121(1):7587.##[6] Chaallal O., Gauthier D., Malenfant P., 1996, Classification methodology for coupled shear walls, Journal of Structural Engineering 122(12):14531458.##[7] Trifunac M. D., Ivanovic S. S., Todorovska M. I., 2001, Apparent periods of a building, Part II: Timefrequency analysis, Journal of Structural Engineering 127( 5):527537.##[8] Goel R. K., Chopra A. K., 1997, Vibration Properties of Buildings Determined from Recorded, Earthquake Engineering Research Center , University of California, Berkeley.##[9] Rutenberg A., 1975, Approximate natural frequencies for coupled shear walls, Earthquake Engineering & Structural Dynamics 4(1):95100.##[10] Wang Y.P., Reinhorn A.M., Soong T.T., 1992, Development of design spectra for actively controlled wall frame buildings , Journal of Engineering Mechanics 118(6):12011220.##[11] Smith S. B., Coull A., 1991, Tall Building Structures: Analysis and Design, Wiley, New York.##[12] Iwan W.D., 1997, Drift spectrum measure of demand for earthquake ground motions, Journal of Structural Engineering 124(4):397404.##[13] Miranda E., Akkar S. D., 2006, Generalised interstorey drift spectrum, Journal of Structural Engineering 132(6):840852.##[14] Miranda E., Reyes C. J., 2002, Approximate lateral drift demands in multistorey buildings with nonuniform stiffness, Journal of Structural Engineering 128(7):840849.##[15] Computer and Structures Inc., 2011, SAP2000 Version 15, Structural Analysis Program, University of Berkeley, California.##]
A New Approach to the Study of Transverse Vibrations of a Rectangular Plate Having a Circular Central Hole
2
2
In this study, the analysis of transverse vibrations of rectangular plate with circular central hole with different boundary conditions is studied and the natural frequencies and natural modes of a rectangular plate with circular hole have been obtained. To solve the problem, it is necessary to use both Cartesian and polar coordinate system. The complexity of the method is to apply an appropriate model, which can solve the problem of transverse vibrations of a plate. So, it has been tried that the functions of the deflection of plate, in the form of polynomial functions proportionate with finite degrees, to be replaced by Bessel function, which is used in the analysis of the vibrations of a circular plate. Then with the help of a semianalytical method and orthogonality properties of the eliminated position angle, without any need to analyze so many points on the edges of the rectangular plate, we can prevent the coefficients matrix from becoming so much large as well as the equations from becoming complicated. The above mentioned functions will lead to reducing the calculation time and simplifying the equations as well as speeding up the convergence.
1

135
149


K
Torabi
Department of Mechanical Engineering, University of Kashan
Department of Mechanical Engineering, University
Iran
kvntrb@kashanu.ac.ir


A.R
Azadi
Department of Mechanical Engineering, University of Kashan
Department of Mechanical Engineering, University
Iran
Transverse vibration analysis
Rectangular plate
Central hole
Bessel function
[[1] Monahan L.J., Nemergut P.J., Maddux G.E., 1970, Natural frequencies and mode shapes of plates with interior cutouts, The Shock and Vibration Bulletin 41:3749.##[2] Paramasivam P., 1973, Free vibration of square plates with square opening, Journal of Sound and Vibration 30:173178.##[3] Aksu G., Ali R., 1976, Determination of dynamic characteristics of rectangular plates with cutouts using a finite difference formulation, Journal of Sound and Vibration 44:147158.##[4] Rajamani A., Prabhakaran R., 1977, Dynamic response of composite plates with cutouts, Part I: SimplySupported Plates, Journal of Sound and Vibration 54:549564.##[5] Rajamani A., Prabhakaran R., 1977, Dynamic response of composite plates with cutouts, Part II: ClampedClamped Plates, Journal of Sound and Vibration 54:565576.##[6] Ali R., Atwal S.J., 1980, Prediction of natural frequencies of vibration of rectangular plates with rectangular cutouts, Computers and Structures 12( 9):819823.##[7] Lam K.Y., Hung K.C, Chow S.T, 1989, Vibration analysis of plates with cutouts by the modified rayleighritz method, Applied Acoustics 28:4960.##[8] Lam K.Y., Hung K.C., 1990, Vibration study on plates with stiffened openings using orthogonal polynomials and partitioning method, Computers and Structures 37:295301.##[9] Laura P.A., Romanelli E., Rossi R.E., 1997, Transverse vibrations of simplysupported rectangular plates with rectangular cutouts, Journal of Sound and Vibration 202(2):275283.##[10] Sakiyama T., Huang M., Matsuda H., Morita C., 2003, Free vibration of orthotropic square plates with a square hole, Journal of Sound and Vibration 259(1):6380.##[11] JogaRao C.V., Pickett G., 1961, Vibrations of plates of irregular shapes and plates with holes, Journal of the Aeronautical Society of India 13(3):8388.##[12] Kumai T., 1952, The flexural vibrations of a square plate with a central circular hole, Proceedings of the Second Japan National Congress for Applied Mechanics .##[13] Hegarty R.F., Ariman T., 1975, Elastodynamic analysis of rectangular plates with circular holes, International Journal of Solids and Structures 11:895906.##[14] Eastep F.E., Hemmig F.G., 1978, Estimation of fundamental frequency of noncircular plates with free, circular cutouts, Journal of Sound and Vibration 56(2):155165.##[15] Nagaya K., 1952, Transverse vibration of a plate having an eccentric inner boundary, Journal of Applied Mechanics 18(3):10311036.##[16] Nagaya K., 1980, Transverse vibration of a rectangular plate with an eccentric circular inner boundary, International Journal of Solids and Structures 16:10071016.##[17] Lee H.S., Kim K.C., 1984, Transverse vibration of rectangular plates having an inner cutout in water, Journal of the Society of Naval Architects of Korea 21(1):2134.##[18] Kim K.C., Han S.Y., Jung J.H., 1987, Transverse vibration of stiffened rectangular plates having an inner cutout, Journal of the Society of Naval Architects of Korea 24(3):3542.##[19] Avalos D.R., Laura P.A., 2003, Transverse vibrations of simply supported rectangular plates with two rectangular cutouts, Journal of Sound and Vibration 267:967977.##[20] Lee H.S., Kim K.C., 1984, Transverse vibration of rectangular plates having an inner cutout in water, Journal of the Society of Naval Architects of Korea 21(1):2134.##[21] Khurasia H.B., Rawtani S., 1978, Vibration analysis of circular plates with eccentric hole, Journal of Applied Mechanics 45(1):215217.##[22] Lin W.H., 1982, Free transverse vibrations of uniform circular plates and membranes with eccentric holes, Journal of Sound and Vibration 81(3):425433.##[23] Laura P.A., Masia U., Avalos D.R., 2006, Small amplitude, transverse vibrations of circular plates elastically restrained against rotation with an eccentric circular perforation with a free edge, Journal of Sound and Vibration 292:10041010.##[24] Cheng L., Li Y.Y., Yam L.H., 2003, Vibration analysis of annularlike plates, Journal of Sound and Vibration 262: 11531170.##[25] Lee W.M., Chen J.T, Lee Y.T., 2007, Free vibration analysis of circular plates with multiple circular holes using indirect BIEMs, Journal of Sound and Vibration 304:811830.##[26] Zhong H., Yu T., 2007, Flexural vibration analysis of an eccentric annular mindlin plate, Archive of Applied Mechanics 77:185195.##[27] Ventsel E., Krauthammer T., 2001, Thin Plates and Shells: Theory, Analysis, and Applications, Marcel Dekker, New York.##[28] Nagaya K., 1980, Transverse vibration of a rectangular plate with an eccentric circular inner boundary, International Journal of Solids and Structures 16:10081016.##]
New Approach to Instability Threshold of a Simply Supported Rayleigh Shaft
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2
The main goal of this research is to analyse the effect of angular velocity on stability and vibration of a simply supported Rayleigh rotating shaft. To this end, nondimensional kinetic and potential energies are written while lateral vibration is considered. Finite element method is employed to discrete the formulations and Linear method is applied to analyse instability threshold of a rotating shaft. These results represent the significant effects of mass moment of inertia, centrifugal forces and rotational speed. Also, the differences between Rayleigh and EulerBernoulli modelling are delivered. Furthermore, the effect of slenderness ratio on instability threshold and the natural frequencies are illustrated. Increasing rotational speed leads to decreasing of instability threshold and forward and backward natural frequencies. These formulations can be used to choose the safe working conditions for a shaft.
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150
157


M
Faraji Mahyari
Department of Mechanical Engineering, Islamic Azad University, Shahre Rey Branch
Department of Mechanical Engineering, Islamic
Iran
farajimahyari@iausr.ac.ir


K.H
Faraji Mahyari
Department of Mechanical Engineering, Islamic Azad University, Shahre Rey Branch
Department of Mechanical Engineering, Islamic
Iran


S
Fardpour
Department of Industrial Design, Islamic Azad University, Shahre Rey Branch
Department of Industrial Design, Islamic
Iran
Rayleigh rotating shaft
Stability
Vibration
Forward and backward natural frequencies
[[1] Grybos R., 1991, Effect of shear and rotary inertia of a rotor at its critical speeds, Archive of Applied Mechanics 61 (2): 104109.##[2] Choi S.H., Pierre C., Ulsoy A. G., 1992, Consistent modelling of rotating timoshenko shafts subject to axial loads, Journal of Vibration, Acoustics, Stress, and Reliability in Design 114 (2):249259.##[3] Jei Y. G., Leh C. W., 1992, Modal analysis of continuous asymmetrical rotorbearing systems, Journal of Sound and Vibration 152 (2):245262.##[4] Singh S. P., Gupta K., 1994, Free damped flexural vibration analysis of composite cylindrical tubes using beam and shell theories, Journal of Sound and Vibration 172 (2):171190.##[5] Kang B., Tan C. A., 1998, Elastic wave motions in an axially strained, infinitely long rotating timoshenko shaft, Journal of Sound and Vibration 213(3):467482.##[6] Jun O. S., Kim J. O., 1999, Free bending vibration of a multistep rotor, Journal of Sound and Vibration 224(4):625642.##[7] Mohiuddin M. A., Khulief Y. A., 1999, Coupled bending torsional vibration of rotors using finite element, Journal of Sound and Vibration 223(2):297316.##[8] Gu U. C., Cheng C. C., 2004, Vibration analysis of a highspeed spindle under the action of a moving mass, Journal of Sound and Vibration 278:11311146.##[9] Behzad M., Bastami A. R., 2004, Effect of centrifugal force on natural frequency of lateral vibration of rotating shafts, Journal of Sound and Vibration 274:985995.##[10] Banerjee J. R., Su H., 2006, Dynamic stiffness formulation and free vibration analysis of a spinning composite beam, Computers and Structures 84:12081214.##[11] Hosseini S.A., Khadem S. E., 2009, Free vibrations analysis of a rotating shaft with nonlinearities in curvature and inertia, Mechanism and Machine Theory 44:272288.##[12] Yigit A. S., Christoforou A. P., 1996, Coupled axial and transverse vibration of oil well drill string, Journal of sound and vibration 195 (4):617627.##[13] Yigit A. S., Christoforou A. P., 1997, Dynamic modelling of rotating drill strings with borehole interactions, Journal of sound and vibration 206(2):243260.##[14] Timoshenko G., 1963, Theory of Elastic Stability, Mc Graw Hill, United state.##[15] Hildebrand F. B., 1984, Methods of Applied Mathematics, Prentice Hall Ind, United state.##[16] Rao J. S., 1983, Rotor Dynamics, New York, John Wiley & Sons, United state.##]
Stress Analysis of Skew Nanocomposite Plates Based on 3D Elasticity Theory Using Differential Quadrature Method
2
2
In this paper, a three dimensional analysis of arbitrary straightsided quadrilateral nanocomposite plates are investigated. The governing equations are based on threedimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straightsided quadrilateral plates but as a special case, the numerical results for skew nanocomposite plates are investigated. The differential quadrature method (DQM) is used to solve these equations. In order to show the accuracy of present work, our results are compared with other numerical solution for skew plates. From the knowledge of author, it is the first time that the stress analysis of arbitrary straightsided quadrilateral nanocomposite plates is investigated. It is shown that increasing the skew angle and thickness of nanocomposite skew plate will decrease the vertical displacements. It is also noted that the thermal effects are also added in the governing equations.
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158
172


M.R
Nami
School of Mechanical Engineering, Shiraz University
School of Mechanical Engineering, Shiraz
Iran


M
Janghorban
School of Mechanical Engineering, Shiraz University
School of Mechanical Engineering, Shiraz
Iran
maziar.janghorban@gmail.com
Straightsided quadrilateral nanocomposite plates
3D elasticity theory
Differential quadrature method
Thermal environment
[[1] Rieth M., Schommers W., 2005, Handbook of Theoretical and Computational Nanotechnology, Basic Concepts, Nanomachines and Bionanodevices, Forschungszentrum Karlsruhe, Germany 1:133.##[2] Shariyat M., Darabi E.A., 2013, Variational iteration solution for elastic–plastic impact of polymer/clay nanocomposite plates with or without global lateral deflection, employing an enhanced contact law, International Journal of Mechanics and Scienc 67:1427.##[3] Jafari Mehrabadi S., Sobhani Aragh B., Khoshkhahesh V., 2012, Mechanical buckling of nanocomposite rectangular plate reinforced by aligned and straight singlewalled carbon nanotubes ,Composite Part B: Engineering 43:20312040.##[4] Belay O.V., Kiselev S.P., 2011, Molecular dynamics simulation of deformation and fracture of a “copper molybdenum” nanocomposite plate under uniaxial tension, Physical Mesomechanics 14:145153.##[5] Yas M.H., Pourasghar A., Kamarian S., 2013, Threedimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube , Material Design 49:583590.##[6] MoradiDastjerdi R., Foroutan M., Pourasghar A., 2013, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a meshfree method, Material Design 44:256266.##[7] Heshmati M., Yas M.H., 2013, Dynamic analysis of functionally graded multiwalled carbon nanotubepolystyrene nanocomposite beams subjected to multimoving loads, Material Design 49:894904.##[8] Shen H.S., Xiang Y., 2013, Postbuckling of nanotubereinforced composite cylindrical shells under combined axial and radial mechanical loads in thermal environment Composite Part B: Engineering 52:311322.##[9] Eftekhari S.A., Jafari A.A., 2013, Modified mixed RitzDQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions , Applied Mathematical Modelling 37(12–13):7398–7426.##[10] Upadhyay A.K., Shukla K.K., 2013, Geometrically nonlinear static and dynamic analysis of functionally graded skew plates, Communications in Nonlinear Science and Numerical Simulation 18:22522279.##[11] Jaberzadeh E., Azhari M., Boroomand B., 2013, Inelastic buckling of skew and rhombic thin thicknesstapered plates with and without intermediate supports using the elementfree Galerkin method, Applied Mathematical Modelling 37(10–11):6838–6854.##[12] Daripa R., Singha M.K., 2009, Influence of corner stresses on the stability characteristics of composite skew plates, International Journal of NonLinear Mechanics 44(2):138146.##[13] Kumar N., Sarcar M.S.R., Murthy M.M.M., 2009, Static analysis of thick skew laminated composite plate with elliptical cutout, Indian Journal of Engineering Material Science 16:3743.##[14] Karami G., Shahpari S.A., Malekzadeh P., 2003, DQM analysis of skewed and trapezoidal laminated plates, Composite Structure 59:393402.##[15] Malekzadeh P., Karami G., 2006, Differential quadrature nonlinear analysis of skew composite plates based on FSDT, Engineering Structure 28(9):13071318.##[16] Malekzadeh P., 2007, A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates, ThinWalled Structure 45(2):237250.##[17] Malekzadeh P., 2008, Differential quadrature large amplitude free vibration analysis of laminated skew plates, on FSDT, Composite Structure 83(2):189200.##[18] Das D., Sahoo P., Saha K.A., 2009, Variational analysis for large deflection of skew under uniformly distributed load through domain mapping technique, International Journal of Engineering Science and Technology 1:1632.##[19] Griebal M., Hamaekers J., 2005, Molecular dynamics simulations of the mechanical properties of polyethylenecarbon nanotube composites, Institut fur Numerische Simulation, Germani.##[20] Malekzadeh P., 2008, Nonlinear free vibration of tapered Mindlin plates with edges elastically restrained against rotation using DQM, ThinWalled Structure 46:1126.##[21] Hashemi M.R., Abedini M.j., Neill S.p., Malekzadeh P., 2008, Tidal and surge modelling using differential quadrature: A case study in the Bristol Channel, Coastal Engineering 55:811819.##[22] Alibeygi Beni A., Malekzadeh P., 2012, Nonlocal free vibration of orthotropic nonprismatic skew nanoplates, Composite Structure 94:32153222.##[23] Malekzadeh P., Heydarpour Y., 2013, Free vibration analysis of rotating functionally graded truncated conical shells, Composite Structure 97:176188.##[24] Sadd M.H., 2009, Elasticity, Theory, Applications, and Numerics, Elsevier.##[25] Griebel M., Hamaekers J., 2004, Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites, Computer Methods in Applied Mechanics and Engineering 193:17731788.##]
Nonlinear Nonlocal Vibration of an Embedded Viscoelastic YSWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method
2
2
In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Yshaped single walled carbon nanotube (YSWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The YSWCNT is also subjected to a longitudinal magnetic field which produces Lorentz force in transverse direction. In order to consider the small scale effects, nonlocal elasticity theory is applied due to its simplicity and accuracy. The smallsize effects and slip boundary conditions of nanoflow are taken into account through Knudsen number (Kn). The YSWCNT is surrounded by elastic medium which is simulated as nonlinear ViscoPasternak foundation. Using energy method and Hamilton’s principle, the nonlinear governing motion equation is obtained. The governing motion equation is solved using both Galerkin procedure and Homotopy analysis method (HAM). Numerical results indicate the significant effects of the mass and velocity of the fluid flow, strength of longitudinally magnetic field, (Kn), angle between the centerline of carbon nanotube and the downstream elbows, nonlocal parameter and nonlinear ViscoPasternak elastic medium. The results of this work is hoped to be of use in design and manufacturing of nanodevices in which Yshaped nanotubes act as basic elements.
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173
193


A
Ghorbanpour Arani
Faculty of Mechanical Engineering, University of Kashan
Institute of Nanoscience & Nanotechnology, University of Kashan
Faculty of Mechanical Engineering, University
Iran
aghorban@kashanu.ac.ir


M.Sh
Zarei
Faculty of Mechanical Engineering, University of Kashan
Faculty of Mechanical Engineering, University
Iran
Homotopy Analysis Method
Nonlinear viscopasternak foundation
Viscose fluid flow
YSWCNT
Knudsen number (Kn)
[[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354:5658.##[2] Wang B.L., Wang K.F., 2013, Vibration analysis of embedded nanotubes using nonlocal continuum theory, Composites Part B 47:96101.##[3] Fang B., Zhen Y.X., Zhang C.P., Tang Y., 2013, Nonlinear vibration analysis of doublewalled carbon nanotubes based on nonlocal elasticity theory, Applied Mathematical Modelling 37:10961107.##[4] Simsek M., Yurtcu H.H., 2013, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures 97:378386.##[5] Liang F., Su Y., 2013, Stability analysis of a singlewalled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect, Applied Mathematical Modelling 37:68216828.##[6] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., Rahmati A.H., 2013, Electrothermotorsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composites Part B 51:291299.##[7] Ke L.L., Wang Y.S., Wang Z.D., 2012, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory Composite Structures 94:20382047.##[8] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B 407:44584465.##[9] Ghorbanpour Arani A., Kolahchi R., Khoddami Maraghi Z., 2013, Nonlinear vibration and instability of embedded doublewalled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modelling 37:76857707.##[10] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2012, Nonlinear free vibration of sizedependent functionally graded microbeams, International Journal of Engineering Science 50:256267.##[11] Asghari M., Kahrobaiyan H.H., Ahmadian M.T., 2010, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science 48:17491761.##[12] Reddy J.N., 2011, Microstructuredependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59:23832399.##[13] Chena W., Lili M.X., 2012, A model of composite laminated Reddy plate based on new modified couple stress theory, Composite Structures 94:21432156.##[14] Zhao J., Zhou S., Wang B., Wang X., 2012, Nonlinear microbeam model based on strain gradient theory, Applied Mathematical Modelling 36:26742686.##[15] Ramezani S., 2012, A micro scale geometrically nonlinear Timoshenko beam model based on strain gradient elasticity theory, International Journal of NonLinear Mechanics 47:863873.##[16] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54:47034710.##[17] Wang L., 2009, Dynamical behaviors of doublewalled carbon nanotubes conveying fluid accounting for the role of small length scale, Computational Materials Science 45:584588.##[18] Ghavanloo E., Daneshmand F., Rafiei M., 2010, Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, Physica E 42:22182224.##[19] Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of doublewalled carbon nanotubes conveying fluid, Computational Materials Science 45:875880.##[20] Xia W., Wang L., 2010, Vibration characteristics of fluidconveying carbon nanotubes with curved longitudinal shape, Computational Materials Science 49:99103.##[21] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communications 36:833837.##[22] Abdollahian M., Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi, R., Loghman A., 2013, Nonlocal wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM, Physica B 418:115.##[23] Lee H.L., Chang W.J., 2009, Vibration analysis of a viscousfluidconveying singlewalled carbon nanotube embedded in an elastic medium, Physica E 41:529532.##[24] Jannesari H., Emami M.D., Karimpour H., 2012, Investigating the effect of viscosity and nonlocal effects on the stability of SWCNT conveying flowing fluid using nonlinear shell model, Physics Letters A 376:11371145.##[25] Rashidi V., Mirdamadi H.R., Shirani E., 2012, A novel model for vibrations of nanotubes conveying nanoflow, Computational Materials Science 51:347352.##[26] Mirramezani M., Mirdamadi H.R., 2012, Effects of nonlocal elasticity and Knudsen number on fluid–structure interaction in carbon nanotube conveying fluid, Physica E 44:20052015.##[27] Lei X.W., Natsuki T., Shi J.X., Ni Q.Q., 2012, Surface effects on the vibrational frequency of doublewalled carbon nanotubes using the nonlocal Timoshenko beam model, Composites Part B 43:6469.##[28] Ashgharifard Sharabiani P., Haeri Yazdi M.R., 2013, Nonlinear free vibrations of functionally graded nanobeams with surface effects, Composites Part B 45:581586.##[29] Wang L., 2010, Vibration analysis of fluidconveying nanotubes with consideration of surface effects, Physica E 43:437439.##[30] Biro L.P., Horvath Z.E., Mark G.I., Osvath Z., Koos A.A., Santucci S., Kenny J.M., 2004, Carbon nanotube Y junctions: growth and properties, Diamond and Related Materials 13:241249.##[31] Lin R.M., 2012, Nanoscale vibration characterization of multilayered graphene sheets embedded in an elastic medium, Computational Materials Science 53:4452.##[32] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A 373:10621069.##[33] Ghorbanpour Arani A., Zarei M.Sh., Amir S., Khoddami Maraghi Z., 2013, Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model, Physica B 410:188196##[34] Ghorbanpour Arani A., Amir S., 2013, Electrothermal vibration of viscoelastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory, Physica B 419:16.##[35] Eichler A., Moser J., Chaste J., Zdrojek M., WilsonRae I., Bachtold A., 2011, Nonlinear damping in mechanical resonators made from carbon nanotubes and grapheme, Nature Nanotechnology 6:339342.##[36] Pirbodaghi T., Ahmadian M.T., Fesanghary M., 2009, On the homotopy analysis method for nonlinear vibration of beams, Mechanics Research Communications 36:143148.##[37] Moghimi Zand M., Ahmadian M.T., 2009, Application of homotopy analysis method in studying dynamic pullin instability of Microsystems, Mechanics Research Communications 36:851858.##[38] Reddy J.N., Wang C.M., 2004, Dynamics of FluidConveying Beams: Governing Equations and Finite Element Models, Centre for Offshore Research and Engineering National University of Singapore.##[39] Ghorbanpour Arani A., Amir S., 2013, Nonlocal vibration of embedded coupled CNTs conveying fluid under thermomagnetic fields via ritz method, Journal of Solid Mechanics 5:206215.##[40] Gurtin M.E., Murdoch A.I., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57:291323.##[41] Narendar S., Ravinder S., Gopalakrishnan S., 2012, Study of nonlocal wave properties of nanotubes with surface effects, Computational Materials Science 56:179184.##[42] Paidoussis M.P., 1998, FluidStructure Interactions: Slender Structures and Axial Flow, Academic Press, London.##[43] Liao S.J., 2003, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman and Hall, CRC Press, Boca Raton.##[44] Hosseini S.H., Pirbodaghi T., Asghari M., Farrahi G.H., Ahmadian M.T., 2008, Nonlinear free vibration of conservative oscillators with inertia and static type cubic nonlinearities using homotopy analysis method, Journal of Sound and Vibration 316:263273.##]
Inplane Band Gaps in a Periodic Plate with Piezoelectric Patches
2
2
A plate periodically bonded with piezoelectric patches on its surfaces is considered. The differential quadrature element method is used to solve the wave motion equation for the twodimensional periodic structure. The method is very simple and easy to implement. Based on the method, band structures for inplane wave propagating in the periodic piezoelectric plate are studied, from which the frequency band gap is then obtained. Parametric studies are also performed to highlight geometrical and physical parameters on the band gaps. It is found that the thickness of the piezoelectric patches have no effect on the upper bound frequency of the band gap. Physical mechanism is explained for the phenomena. Dynamic simulations are finally conducted to show how the band gap works for a finite quasiperiodic plate. Numerical results show that the vibration in periodic plates can be dramatically attenuated when the exciting frequency falls into the band gap.
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194
207


H.J
Xiang
School of Civil Engineering, Beijing Jiaotong University
School of Civil Engineering, Beijing Jiaotong
Iran
hjxiang@bjtu.edu.cn


Z.B
Cheng
School of Civil Engineering, Beijing Jiaotong University
School of Civil Engineering, Beijing Jiaotong
Iran


Z.F
Shi
School of Civil Engineering, Beijing Jiaotong University
School of Civil Engineering, Beijing Jiaotong
Iran


X.Y
Yu
School of Civil Engineering, Beijing Jiaotong University
School of Civil Engineering, Beijing Jiaotong
Iran
Band gap
Piezoelectric
Differential quadrature element method
Periodic materials
Plate
[[1] Sigalas M., Kushwaha M.S., Economou E.N., Kafesaki M., Psarobas I.E., Steurer W., 2005, Classical vibrational modes in phononic lattices: theory and experiment, Zeitschrift für Kristallographie 220:765809.##[2] Baz A., 2001, Active control of periodic structures, Journal of Vibration and Acoustic 123: 472479.##[3] Kushwaha M.S., Halevi P., Dobrzynski L., DjafariRouhani B., 1993, Acoustic band structure of periodic elastic composites, Physical Review Letters 71(13): 20222025.##[4] Kushwaha M.S., Halevi P., 1994, Band gap engineering in periodic elastic composites, Applied Physics Letters 64(9): 10851087.##[5] Liu Z., Zhang X., Mao Y., Zhu Y.Y., Yang Z., Chan C.T., Sheng P., 2000, Locally resonant sonic materials, Science 289(5485): 17341736.##[6] Jia G., Shi Z., 2010, A new seismic isolation system and its feasibility study, Earthquake Engineering and Engineering Vibration 9(1): 7582.##[7] Bao J., Shi Z.F., Xiang H.J., 2012, Dynamic responses of a structure with periodic foundations, Journal of Engineering MechanicsASCE 138(7): 761769.##[8] Xiang H.J., Shi Z.F., Wang S.J., Mo Y.L., 2012, Periodic materialsbased vibration attenuation in layered foundations: experimental validation, Smart Materials and Structures 21(11): 112003.##[9] Xiong C., Shi Z.F., Xiang H.J., 2012, Attenuation of building vibration using periodic foundations, Advances in Structural Engineering 15(8): 13751388.##[10] Khelif A., DjafariRouhani B., Vasseur J.O., Deymier P.A., Lambin P., Dobrzynski L., 2002, Transmittivity through straight and stublike waveguides in a twodimensional phononic crystal, Physical Review B 65(17): 174308.##[11] Khelif A., Aoubiza B., Mohammadi S., Adibi A., Laude V., 2006, Complete band gaps in twodimensional phononic crystal slabs, Physical Review E 74(4): 046610.##[12] Thorp O., Ruzzene M., Baz A., 2001, Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches, Smart Materials and Structures 10: 979.##[13] Wang Y.Z., Li F.M., Kishimoto K., Wang Y.S., Huang W.H., 2009, Wave band gaps in threedimensional periodic piezoelectric structures, Mechanics Research Communications 36(4): 461468.##[14] Wu T.T., Hsu Z.C., Huang Z.G., 2005, Band gaps and the electromechanical coupling coefficient of a surface acoustic wave in a twodimensional piezoelectric phononic crystal, Physical Review B 71(6): 064303.##[15] Zou X.Y., Chen Q., Liang B., Cheng J.C., 2008, Control of the elastic wave bandgaps in twodimensional piezoelectric periodic structures, Smart Materials and Structures 17: 015008.##[16] Xiang H.J., Shi Z.F., 2009, Analysis of flexural vibration band gaps in periodic beams using differential quadrature method, Computers & Structures 87(2324): 15591566.##[17] Xiang H.J., Shi Z.F., 2011, Vibration attenuation in periodic composite Timoshenko beams on Pasternak foundation, Structural Engineering and Mechanics 40(3): 373392.##[18] Kittel C., 2005, Introduction to Solid State Physics, John Wiley & Son, New York, 8th Edition.##[19] Chen C.N., 2004, Extended GDQ and related discrete element analysis methods for transient analyses of continuum mechanics problems, Computers & Mathematics with Applications 47(1): 9199.##[20] Chen C.N., 2008, DQEM analysis of outofplane vibration of nonprismatic curved beam structures considering the effect of shear deformation, Advances in Engineering Software 39(6): 466472.##[21] Malekzadeh P., Karami G., Farid M., 2004, A semianalytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported, Computer Methods in Applied Mechanics and Engineering 193(4547): 47814796.##[22] Liu F.L., Liew K.M., 1999, Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities, Computer Methods in Applied Mechanics and Engineering 179(3): 407423.##[23] Eisinberg A., Fedele G., 2005, Vandermonde systems on gausslobatto chebyshev nodes, Applied Mathematics and Computation 170(1): 633647.##[24] Shu C., 2000, Differential Quadrature: And Its Application in Engineering, Springer, London.##[25] Shu C., Richards B.E., 1992, Application of generalized differential quadrature to solve twodimensional incompressible NavierStokes equations, International Journal for Numerical Methods in Fluids 15(7): 791798.##[26] Xiang H.J., Yang J., 2008, Free and forced vibration of a laminated FGM timoshenko beam of variable thickness under heat conduction, Composites Part BEngineering 39(2): 292303.##[27] Yang J., Xiang H.J., 2007, Thermoelectromechanical characteristics of functionally graded piezoelectric actuators, Smart Materials and Structures 16(3): 784797.##[28] Wen X.S., Wen J.H., Yu D.L., Wang G., Liu Y.Z., Han X.Y., 2009, Phononic Crystals, Ational Defense Industry Press, Beijing.##[29] Åberg M., Gudmundson P., 1997, The usage of standard finite element codes for computation of dispersion relations in materials with periodic microstructure, The Journal of the Acoustical Society of America 102(4): 20072013.##[30] Yaman Y., Çalışkan T., Nalbantoğlu V., Prasad E., Waechter D., 2002, Active Vibration Control of a Smart Plate, ICAS2002, Toronto, Canada.##]
Numerical Simulation of SemiElliptical Axial Crack in Pipe Bend Using XFEM
2
2
In this work, XFEM is employed to obtain the stress intensity factors (SIFs) of a semi elliptical part through thickness axial crack. In XFEM, additional functions are employed to enrich the displacement approximation using partition of unity approach. Level set functions are approximated using higher order shape functions in the crack front elements to ensure the accurate modeling of the crack. The axial crack is placed either on the inner or the outer surface in an internally pressurized pipe bend. The SIFs are extracted from XFEM solution by domain type interaction integral approach for a wide range of geometry parameters like bend radius ratio, cross sectional radius ratio and relative crack length. The results obtained by XFEM approach are compared with those obtained by FEM. These simulations show that the orientation and type of crack in pipe bend has a significant effect on the SIF.
1

208
228


K
Sharma
Reactor Structures Section, Reactor Safety Division, BARC, Mumbai, India
Reactor Structures Section, Reactor Safety
Iran
kunal_nit90@rediffmail.com


I.V
Singh
Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee
Department of Mechanical and Industrial Engineerin
Iran
ivsingh@gmail.com


B.K
Mishra
Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee
Department of Mechanical and Industrial Engineerin
Iran


S.K
Maurya
Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee
Department of Mechanical and Industrial Engineerin
Iran
Elliptical cracks
Pipe bend
SIFs
XFEM
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P. , Alturi S. N., 1987, Calculation of fracture mechanics parameters for an arbitrary threedimensional crack by the equivalent domain integral method, International Journal for Numerical Methods in Engineering 24: 18011821.##[16] Rhee H. C., Salama M. M., 1987, Mixedmode stress intensity factor solutions of a warped surface flaw by threedimensional finite element analysis, Engineering Fracture Mechanics 28: 203209.##[17] Portela A., Aliabadi M., Rooke D., 1991, The dual boundary element method: effective implementation for crack problem, International Journal for Numerical Methods in Engineering 33: 12691287.##[18] Yan A. M., NguyenDang H., 1995, Multiplecracked fatigue crack growth by BEM, Computational Mechanics 16: 273280.##[19] Belytschko T., Gu L., Lu Y.Y., 1994, Fracture and crack growth by elementfree Galerkin methods, Modelling Simulation for Materials Science and Engineering 2: 519534.##[20] Belytschko T., Lu Y.Y., Gu L., 1995, Crack propagation by elementfree Galerkin methods, Engineering Fracture Mechanics 51: 295315.##[21] Belytschko T., Black T., 1999, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45: 601620.##[22] Dolbow J., 1999, An extended finite element method with discontinuous enrichment for applied mechanics, Theoretical and Applied Mechanics Department, Northwestern University.##[23] Moës N., Dolbow J., Belytchsko T., 1999, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46: 131150.##[24] Daux C., Moës N., Dolbow J., Sukumar N., Belytschko T., 2000, Arbitrary branched and intersecting cracks with the extended finite element method, International Journal for Numerical Methods in Engineering 48: 17411760.##[25] Sukumar N., Chopp D.L., Moës N., Belytschko T., 2001, Modeling holes and inclusions by level sets in the extended finiteelement method, Computer Methods in Applied Mechanics and Engineering 190: 61836200.##[26] Sukumar N., Moës N., Moran B., Belytschko T., 2000, Extended finite element method for threedimensional crack modelling, International Journal for Numerical Methods in Engineering 48: 15491570.##[27] Moës N., Gravouil A., Belytschko T., 2002, Nonplanar 3D crack growth by the extended finite element and level setsPart I: Mechanical model, International Journal for Numerical Methods in Engineering 53: 25492568.##[28] Gravouil A., Moës N., Belytschko T., 2002, Nonplanar 3D crack growth by the extended finite element and level setsPart II: Level set update, International Journal for Numerical Methods in Engineering 53: 25692586.##[29] Sharma K., Bhasin V., Singh I.V., Mishra B.K., Vaze K.K., XFEM simulation of 2D fracture mechanics problems, SMiRT21, New Delhi, India.##[30] Pathak H., Singh A., Singh I.V., Yadav S. K., 2013, A simple and efficient XFEM approach for 3D cracks siluations, Internationa Journal of Fracture 181: 189208.##[31] Melenk J., Babuska I., 1996, The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering 139: 289314.##[32] Zi G., Belytschko T., 2003, New cracktip elements for XFEM and applications to cohesive cracks, International Journal for Numerical Methods in Engineering 57: 22212240.##[33] Sukumar N., Chopp D.L., Moran B., 2003, Extended finite element method and fast marching method for threedimensional fatigue crack propagation, Engineering Fracture Mechanics 70: 2948.##[34] Moran B., Shih C., 1987, A general treatment of crack tip contour integrals, International Journal of Fracture 35: 295310.##[35] Shih C.F., Asaro R.J., 1988, Elasticplastic analysis of cracks on bimaterial interfaces: Part Ismall scale yielding, Journal of Applied Mechanics 55: 299316.##[36] Gosz M., Dolbow J., Moran B., 1998, Domain integral formulation for stress intensity factor computation along curved threedimensional interface cracks, International Journal of Solids and Structures 35: 17631783.##[37] Gosz M., Moran B., 2002, An interaction energy integral method for computation of mixedmode stress intensity factors along nonplanar crack fronts in three dimensions, Engineering Fracture Mechanics 69: 299319.##]
Reflection of Waves in a Rotating Transversely Isotropic Thermoelastic Halfspace Under Initial Stress
2
2
The present paper concerns with the effect of initial stress on the propagation of plane waves in a rotating transversely isotropic medium in the context of thermoelasticity theory of GN theory of typeII and III. After solving the governing equations, three waves propagating in the medium are obtained. The fastest among them is a quasilongitudinal wave. The slowest of them is a thermal wave. The remaining is called quasitransverse wave. The prefix ‘quasi’ refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these three waves are not mutually orthogonal. After imposing the appropriate boundary conditions, the amplitudes of reflection coefficients have been obtained. Numerically, simulated results have been plotted graphically with respect to frequency to evince the effect of initial stress and anisotropy.
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229
239


R.R
Gupta
Department of CS & IT Mazoon University College, Muscat, Oman
Department of CS & IT Mazoon University
Iran
raji.mmec@gmail.com


R.R.
Gupta
Department of Mathematics, MEC, Muscat, Oman
Department of Mathematics, MEC, Muscat, Oman
Iran
Rotation
Amplitude ratios
Initial stress
Thermoelasticity
Reflection
Plane wave
[[1] Biot M. A., 1965, Mechanics of Incremental Deformations, John Wiley, New York.##[2] Chandrasekhariah D. S., 1998, Hyperbolic thermoelasticity: a review of recent literature, Applied Mechanics Reviews 51:705729.##[3] Chandrasekharaiah D. S., Srinath K. S., 1996, Onedimensional waves in a thermo elastic halfspace without energy dissipation, International Journal of Engineering Science 34:14471455.##[4] Chandrasekharaiah D. S., Srinath K. S., 1997, Axisymmetric thermoelastic inter actions without energy dissipation in an unbounded body with cylindrical cavity, Journal of Elasticity 46:1931.##[5] Chand D., Sharma J.N., Sud S.P., 1990, Transient generalized magnetothermoelastic waves in a rotating half space, International Journal of Engineering Science 28:547556.##[6] Chattopadhyay A., Bose S., Chakraborty M., 1982, Reflection of elastic waves under initial stress at a free surface, Journal of Acoustical Society of America 72: 255263.##[7] Clarke N.S., Burdness J.S., 1994, Rayleigh waves on a rotating surface, Journal of Applied Mechanics,Transactions of ASME 61:724726.##[8] Destrade M., 2004, Surface waves in rotating rhombic crystal, Proceeding of the Royal Society A 460 :653665.##[9] Dey S., Roy N., Dutta A., 1985, Reflection and refraction of pwaves under initial stresses at an interface, Indian Journal of Pure and Applied Mathematics16:10511071.##[10] Dhaliwal R.S., Singh A., 1980, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India.##[11] Green A.E., Lindsay K. A., 1972, Thermoelasticity, Journal of Elasticity 2:15.##[12] Green A.E., Naghdi P.M., 1991, A reexamination of the basic postulates of thermomechanics, Proceedings of the Royal Society of London Series A 432:171194.##[13] Green A.E., Naghdi P. M., 1992, On undamped heat waves in an elastic solid, Journal of Thermal Stresses 15:253264.##[14] Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity 31:189208.##[15] Gupta R. R., 2011, Propagation of waves in the transversely isotropic thermoelastic Green and Naghdi typeII and typeIII medium, Journal of Applied Mechanics and Technical Physics 52(5):825833.##[16] Gupta R.R.,2013, Reflection of waves in viscothermoelastic transversely isotropic medium, International Journal for Computational Methods in Engineering Science and Mechanics 14: 8389.##[17] Gupta R. R., Gupta R. R., 2013, Analysis of wave motion in an initially stressed anisotropic fiberreinforced thermoelastic medium, Earthquakes and Structures 4(1):110.##[18] Gupta R. R., Gupta R. R., 2013, Reflection of waves in initially stressed transversely isotropic fibrereinforced thermoelastic medium, International Journal of Advances in Management and Economics 18(3): 671685.##[19] Hetnarski R.B., Iganazack J., 1999, Generalised thermoelasticity, Journal of Thermal Stresses 22:451470.##[20] Lord H., Shulman Y.A., 1967, Generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299309.##[21] Mahmoud S. R., 2011, Effect of rotation, gravity field and initial stress on generalized magnetothermoelastic rayleigh waves in a granular medium, Applied Mathematical Sciences 5(41):20132032.##[22] Montanaro A., 1999, On singular surface in isotropic linear thermoelasticity with initial stress, Journal of Acoustical Society of America 106:1586–1588.##[23] Othman M.I.A., Song Y., 2007, Reflection of plane waves from an elastic solid halfspace under hydrostatic initial stress without energy dissipation, International Journal of Solids and Structures 44:56515664.##[24] Othman M.I.A., 2008, Effect of rotation on plane waves in generalized thermoelasticity with two relaxation times, International Journal of Solids and Structures 41:29392956.##[25] Othman M.I.A., Song Y., 2007, Reflection of plane waves from an elastic solid halfspace under hydrostatic initial stress without energy dissipation, International Journal of Solids and Structures 44:56515664.##[26] Othman M.I.A., Song Y., 2008, Reflection of magnetothermo elastic waves from a rotating elastic halfspace, International Journal of Engineering Sciences 46:459474.##[27] Othman M.I.A., Song Y., 2009, The effect of rotation on 2d thermal shock problems for a generalized magnetothermoelasticity halfspace under three theories, Multidiscipline Modeling in Mathematics and Structures 5:4358.##[28] Schoenberg M., Censor D., 1973, Elastic waves in rotating media, Quarterly of Applied Mathematics 31:115125.##[29] Sharma J.N., 2007, Effect of rotation on rayleighlamb waves in piezothermoelastic half space, International Journal of Solids and Structures 44:10601072.##[30] Sidhu R.S., Singh S.J., 1983, Comments on “reflection of elastic waves under initial stress at a free surface”, Journal of Acoustical Society of America 74:16401642.##[31] Singh B., 2008, Effect of hydrostatic initial stresses on waves in a thermoelastic solid halfspace, Journal of Applied Mathematics and Computation 198:494505.##[32] Singh B. B., Kumar A., Singh J., 2006, Reflection of generalized thermoelastic waves from a solid halfspace under hydrostatic initial stress, Journal of Applied Mathematics and Computation 177:170177.##[33] Slaughter W. S., 2002, The Linearized Theory of Elasticity, Birkhauser.##]