Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 A Mathematical Formulation to Estimate the Fundamental Period of High-Rise Buildings Including Flexural-Shear Behavior and Structural Interaction 122 134 EN E Noroozinejad Farsangi Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology, Tehran ehsan.noroozinejad@gmail.com H Melatdoust Multimedia University, Cyberjaya, Malaysia A Bin Adnan Civil Engineering Department, University of Technology Malaysia, Johor Bahru, Malaysia 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 Sturm-Liouville 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 forth-order Sturm-Liouville 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 earthquake-induced 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 time-consuming procedure of handling all the data can always be a source of errors. Fundamental period,continuum,FEA,4th order sturm-liouville differential equation http://jsm.iau-arak.ac.ir/article_514591.html http://jsm.iau-arak.ac.ir/article_514591_4fc46283260b64f7cf091a9ce7a893c8.pdf
Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 A New Approach to the Study of Transverse Vibrations of a Rectangular Plate Having a Circular Central Hole 135 149 EN K Torabi Department of Mechanical Engineering, University of Kashan kvntrb@kashanu.ac.ir A.R Azadi Department of Mechanical Engineering, University of Kashan 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 semi-analytical 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. Transverse vibration analysis,Rectangular plate,Central hole,Bessel function http://jsm.iau-arak.ac.ir/article_514592.html http://jsm.iau-arak.ac.ir/article_514592_f5c9e9cf3f21c6d4247d128b00334773.pdf
Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 New Approach to Instability Threshold of a Simply Supported Rayleigh Shaft 150 157 EN M Faraji Mahyari Department of Mechanical Engineering, Islamic Azad University, Shahr-e Rey Branch farajimahyari@iausr.ac.ir K.H Faraji Mahyari Department of Mechanical Engineering, Islamic Azad University, Shahr-e Rey Branch S Fardpour Department of Industrial Design, Islamic Azad University, Shahr-e Rey Branch 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, non-dimensional 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 Euler-Bernoulli 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. Rayleigh rotating shaft,Stability,Vibration,Forward and backward natural frequencies http://jsm.iau-arak.ac.ir/article_514593.html http://jsm.iau-arak.ac.ir/article_514593_336bfb1bc7497a1c905138012c42f6ca.pdf
Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 Stress Analysis of Skew Nanocomposite Plates Based on 3D Elasticity Theory Using Differential Quadrature Method 158 172 EN M.R Nami School of Mechanical Engineering, Shiraz University M Janghorban School of Mechanical Engineering, Shiraz University maziar.janghorban@gmail.com In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided 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 straight-sided 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. Straight-sided quadrilateral nanocomposite plates,3D elasticity theory,Differential quadrature method,Thermal environment http://jsm.iau-arak.ac.ir/article_514594.html http://jsm.iau-arak.ac.ir/article_514594_97fab790471c553b8289678fdac35bf7.pdf
Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method 173 193 EN A Ghorbanpour Arani Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan aghorban@kashanu.ac.ir M.Sh Zarei Faculty of Mechanical Engineering, University of Kashan In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT 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 small-size effects and slip boundary conditions of nano-flow are taken into account through Knudsen number (Kn). The Y-SWCNT is surrounded by elastic medium which is simulated as nonlinear Visco-Pasternak 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 Visco-Pasternak elastic medium. The results of this work is hoped to be of use in design and manufacturing of nano-devices in which Y-shaped nanotubes act as basic elements. Homotopy Analysis Method,Nonlinear visco-pasternak foundation,Viscose fluid flow,Y-SWCNT,Knudsen number (Kn) http://jsm.iau-arak.ac.ir/article_514595.html http://jsm.iau-arak.ac.ir/article_514595_678411c6e1abf2afc392ebed15d97d55.pdf
Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 In-plane Band Gaps in a Periodic Plate with Piezoelectric Patches 194 207 EN H.J Xiang School of Civil Engineering, Beijing Jiaotong University hjxiang@bjtu.edu.cn Z.B Cheng School of Civil Engineering, Beijing Jiaotong University Z.F Shi School of Civil Engineering, Beijing Jiaotong University X.Y Yu School of Civil Engineering, Beijing Jiaotong University 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 two-dimensional periodic structure. The method is very simple and easy to implement. Based on the method, band structures for in-plane 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 quasi-periodic plate. Numerical results show that the vibration in periodic plates can be dramatically attenuated when the exciting frequency falls into the band gap.                                                   Band gap,Piezoelectric,Differential quadrature element method,Periodic materials,Plate http://jsm.iau-arak.ac.ir/article_514596.html http://jsm.iau-arak.ac.ir/article_514596_d8e2587a9a4c83e8cb99d96ce363800a.pdf
Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 Numerical Simulation of Semi-Elliptical Axial Crack in Pipe Bend Using XFEM 208 228 EN K Sharma Reactor Structures Section, Reactor Safety Division, BARC, Mumbai, India kunal_nit90@rediffmail.com I.V Singh Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee ivsingh@gmail.com B.K Mishra Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee S.K Maurya Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee 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. Elliptical cracks,Pipe bend,SIFs,XFEM http://jsm.iau-arak.ac.ir/article_514597.html http://jsm.iau-arak.ac.ir/article_514597_2e0b7c773df559dfca504d9adeab42cd.pdf
Islamic Azad University - Arak Branch Journal of Solid Mechanics 2008-3505 2008-7683 6 2 2014 06 30 Reflection of Waves in a Rotating Transversely Isotropic Thermoelastic Half-space Under Initial Stress 229 239 EN R.R Gupta Department of CS & IT Mazoon University College, Muscat, Oman raji.mmec@gmail.com R.R. Gupta Department of Mathematics, MEC, Muscat, Oman 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 type-II and III. After solving the governing equations, three waves propagating in the medium are obtained. The fastest among them is a quasi-longitudinal wave. The slowest of them is a thermal wave. The remaining is called quasi-transverse 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.                                                  Rotation,Amplitude ratios,Initial stress,Thermoelasticity,Reflection,Plane wave http://jsm.iau-arak.ac.ir/article_514598.html http://jsm.iau-arak.ac.ir/article_514598_e7f1597a6f61cc696979e5306624ea9e.pdf