eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
464
475
544388
Vibration Analysis of FG Nanoplate Based on Third-Order Shear Deformation Theory (TSDT) and Nonlocal Elasticity
M.M Najafizadeh
m-najafizadeh@iau-arak.ac.ir
1
M Raki
2
P Yousefi
3
Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran
In present study, the third-order shear deformation theory has been developed to investigate vibration analysis of FG Nano-plates based on Eringen nonlocal elasticity theory. The materials distribution regarding to the thickness of Nano-plate has been considered based on two different models of power function and exponential function. All equations governing on the vibration of FG Nano-plate have been derived from Hamilton’s principle. It has been also obtained the analytical solution for natural frequencies and corresponding mode shapes of simply supported FG Nano-plates. In addition, the general form of stiffness and mass matrix elements has been expressed based on this theory. The effect of different parameters such as power and exponential indexes of targeted function , nonlocal parameter of Nano-plate, aspect ratio and thickness to length ratio of Nano-plate on non-dimensional natural frequencies of free vibration responses have been investigated. The obtained analytical results show an excellent agreement with other available solutions of previous studies. The formulation and analytical results obtained from proposed method can be used as a benchmark for further studies to develop this area of research.
http://jsm.iau-arak.ac.ir/article_544388_6076a1d0233da7aa5c146d92c451b4fb.pdf
Nano-plate
Functionally graded material (FGM)
Nonlocal elasticity
Third order of shear deformation theory (TSDT)
Natural frequency
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
476
488
544389
Mechanical Buckling Analysis of Composite Annular Sector Plate with Bean-Shaped Cut-Out using Three Dimensional Finite Element Method
H Behzad
1
A.R Shaterzadeh
a_shaterzadeh@shahroodut.ac.ir
2
M Shariyat
3
Faulty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
Faulty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
In this paper, mechanical buckling analysis of composite annular sector plates with bean shape cut out is studied. Composite material sector plate made of Glass-Epoxy and Graphite-Epoxy with eight layers with same thickness but different fiber angles for each layer. Mechanical loading to form of uniform pressure loading in radial, environmental and biaxial directions is assumed. The method used in this analysis is three dimensional (3D) finite elements based on the elasticity relations. With zero first and second variation of potential energy of the entire annular sector plate, we find stability equation. Green non-linear displacement strain relations to obtain geometric stiffness matrix is used. Unlike many studies, in present work three dimensional finite elements method has been used with an eight node element and meshing in the thickness direction is done, too. The bean shaped cut out in the sector has increased the complexity of the analysis. The continuing, effect of different parameters including cut out dimensions, fiber angles of layers, loading direction and dimensions of the annular sector plate on the mechanical buckling load has been investigated and interesting results have been obtained.
http://jsm.iau-arak.ac.ir/article_544389_6012ddbbb6c28bef4d3e7cc69874f32f.pdf
Annular sector plate
Composite material
3D finite elements method
Mechanical buckling
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
489
501
544390
Influences of Small-Scale Effect and Boundary Conditions on the Free Vibration of Nano-Plates: A Molecular Dynamics Simulation
S.F Asbaghian Namin
1
R Pilafkan
rezapilafkan@um.ac.ir
2
University of Mohaghegh Ardabili, Ardabil, Iran
University of Mohaghegh Ardabili, Ardabil, Iran
This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the most common nano-plates. On the other hand, governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different side lengths, boundary conditions, and nonlocal parameter are inspected for the aforementioned methods. The results obtained from the MD simulations are compared with those of nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. As a result, for the first time, the nonlocal parameter values are suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.
http://jsm.iau-arak.ac.ir/article_544390_467c7d1172c85cae10c3815b276a67bf.pdf
Nano-plates
Molecular dynamics simulations
Fundamental frequencies
Nonlocal elasticity theory
Nonlocal parameter
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
502
521
544391
3D Thermoelastic Interactions in an Anisotropic Lastic Slab Due to Prescribed Surface Temparature
Gh Debkumar
debkumarghosh2020@gmail.com
1
L Abhijit
2
R Kumar
rajneesh_kuk@rediffmail.com
3
R Surath
4
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Kurukshetra University, India
Department of Mathematics, Brainware College of Engineering, Barasat, Kolkata, India
The present paper is devoted to the determination of displacement, stresses and temperature from three dimensional anisotropic half spaces due to presence of heat source. The normal mode analysis technique has been used to the basic equations of motion and generalized heat conduction equation proposed by Green-Naghdi model-II [1]. The resulting equation are written in the form of a vector –matrix differential equation and exact expression for displacement component, stresses, strains and temperature are obtained by using eigen value approach. Finally, temperature, stresses and strain are presented graphically and analyzed.
http://jsm.iau-arak.ac.ir/article_544391_026249e057ade954bc4ef8f7c543061a.pdf
eigenvalue
Generalized thermoelasticity
Normal mode analysis and vector-matrix
Differential equation
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
522
531
544392
Failure Criteria Analysis of Laminate Composite Materials
L Nourine
mechanics151@yahoo.com
1
A Sahli
2
S Sahli
3
Laboratoire de Mécanique Appliquée, Université des Sciences et de la Technologie d’Oran , Algéira
Laboratoire de Recherche des Technologies Industrielles, Université Ibn Khaldoun de Tiaret, Algéira
Département de Génie Mécanique, Université d’Oran, Algéira
This paper deals with the development of a numerical simulation methodology for estimating damages in laminate composite materials caused by a low-speed impact. Experimental tests were performed on laminate plates reinforced with woven carbon fibers and epoxy resin. Three thickness plates were evaluated. The impact loads were transversal and punctual. Two lamina failure criteria were evaluated. The first is the maximum stress. The second is a proposed modification of the Hashin failure criterion. Four lamina degradation criteria were evaluated too. The numerical contact loads between the plate and impactor were well represented. The numerical damaged areas and lengths were similar or greater than the experimental results.
http://jsm.iau-arak.ac.ir/article_544392_56b7a39ceee809074d38fca1b4286094.pdf
Criterion damage
Failure criteria
Impact
Laminate composite materials
Damage strength
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
532
546
544401
Extraction of Nonlinear Thermo-Electroelastic Equations for High Frequency Vibrations of Piezoelectric Resonators with Initial Static Biases
M.M Mohammadi
dr.mohamamdi@gmail.com
1
M Hamedi
mhamedi@ut.ac.ir
2
H Daneshpajooh
3
School of Mechanical Engineering, College of Engineering, University of Zanjan, Zanjan, Iran
College of Mechanical Engineering, University of Tehran, Tehran, Iran
Department of Electrical Engineering, Pennsylvania State University, USA
In this paper, the general case of an anisotropic thermo-electro elastic body subjected to static biasing fields is considered. The biasing fields may be introduced by heat flux, body forces, external surface tractions, and electric fields. By introducing proper thermodynamic functions and employing variational principle for a thermo-electro elastic body, the nonlinear constitutive relations and the nonlinear equation of motion are extracted. The equations have the advantage of employing the Lagrangian strain and second Piola-Kirchhoff stress tensor with symmetric characteristics. These equations are used to analyze the high frequency vibrations of piezoelectric resonators under finite biasing fields. A system of three dimensional equations is derived for initial and incremental fields on the body. Capability of the equations in numerical modelling of temperature-frequency and force-frequency effects in quartz crystal is demonstrated. The numerical results compare well with the data from experiments. These equations may be used in accurate modelling of piezoelectric devices subjected to thermo electro mechanical loads.
http://jsm.iau-arak.ac.ir/article_544401_f40e1d8916a21beaf474daf95dc235f4.pdf
Nonlinear Equations
Thermo-electro elasticity
Initial static bias
Resonators
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
547
560
544402
Shape- Dependent Term Investigation of Khan- Liu Yield/ Fracture Criterion as a Function of Plastic Strain for Anisotropic Metals
F Farhadzadeh
1
M Tajdari
me-tajdari@iau-arak.ac.ir
2
M Salmani Tehrani
3
Marine Department, Malek-Ashtar University of Technology, Isfahan, Iran
Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
The current paper primarily aims to suggest a mathematical model for the shape-dependent term of Khan- Liu (KL) Yield/ fracture criterion as a function of Plastic Strain for DP590 steel alloy. The shape-dependent term in the mention criterion can generalize the application of this criterion in order to predict the behavior of other materials. Plane stress case and the first quarter of the stress plane have been specifically studied. Uniaxial stresses in rolling and transverse directions of sheet and also the tensions caused by equal-biaxial tension have been experimentally used. Then, material constants of KL yield/ fracture criterion and Khan- Huang- Liang (KHL) constitutive equation are calculated using genetic algorithm (GA) optimization and the value of the shape-dependent factor in KL criterion is extracted. The same has been repeated for various plastic strains and finally a polynomial mathematical model based on the plastic strain for the KL shape-dependent factor is suggested. Hence, material constants of KL criterion could be calculated using at least tests namely experimental uniaxial stress test, experimental equal-biaxial stress, and one of the optimization models such as GA. Using the given mathematical model based on the plastic strain, correction term can be calculated and the generalized form of KL criterion can be used for various ductile metallic materials.
http://jsm.iau-arak.ac.ir/article_544402_26c7b38ea6c7ad2482d23ebb428e2f3e.pdf
Yield/ fracture criterion
Constitutive equation
Shape-dependent term
Cruciform specimen
DP590 Steel alloy
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
561
570
544403
New Method for Large Deflection Analysis of an Elliptic Plate Weakened by an Eccentric Circular Hole
Sh Dastjerdi
dastjerdi_shahriar@yahoo.com
1
L Yazdanparast
2
Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Department of Mechanical Engineering, Damavand Branch, Islamic Azad University, Damavand, Iran
The bending analysis of moderately thick elliptic plates weakened by an eccentric circular hole has been investigated in this article. The nonlinear governing equations have been presented by considering the von-Karman assumptions and the first-order shear deformation theory in cylindrical coordinates system. Semi-analytical polynomial method (SAPM) which had been presented by the author before has been used. By applying SAPM method, the nonlinear partial differential equations have been transformed to the nonlinear algebraic equations system. Then, the nonlinear algebraic equations have been solved by using Newton–Raphson method. The obtained results of this study have been compared with the results of other references and the accuracy of the results has been shown. The effect of some important parameters on the results such as the location of the circular hole, the ratio of major to minor radiuses of elliptical plate, the size of circular hole and boundary conditions have been studied. It is concluded that applying the presented method is very convenient and efficient. So, it can be used for analyzing the mechanical behavior of elliptical plates, instead of relatively complicated formulations in elliptic coordinates system.
http://jsm.iau-arak.ac.ir/article_544403_3bc6d0710e1f14a64435dfe287fd8a1b.pdf
Elliptical plate
Eccentric circular hole
First-order shear deformation theory
Semi-analytical polynomial method (SAPM)
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
571
580
544405
A Contact Problem of an Elastic Layer Compressed by Two Punches of Different Radii
K Seghir
1
M Bendaoui
2
R Benbouta
r_benbouta@yahoo.fr
3
Department of Mechanical Engineering, Faculty of Technology, University of Batna2, Algeria
Department of Mechanical Engineering, Faculty of Technology, University of Batna2, Algeria
Department of Mechanical Engineering, Faculty of Technology, University of Batna2, Algeria
The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of an isotropic elastic layer compressed by two rigid cylinders with flat ends. Hankel transformation and auxiliary functions with boundary conditions reduce the differential equation to an algebraic equations system, which can be solved in a numerical way. The contact efforts equations are established. From the general method, solutions of particular cases are also resolved. A particular case is studied, the contact zone pressure and stresses distribution curves are presented.
http://jsm.iau-arak.ac.ir/article_544405_e80ab934b64c5db455455a4bad66f285.pdf
Keywords: Contact problem
Elastic layer
Cylindrical punches
Flat ends
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
581
590
544407
Torsion in Microstructure Hollow Thick-Walled Circular Cylinder Made up of Orthotropic Material
S Yadav
sneh.mathematics@gmail.com
1
S Sharma
2
Department of Mathematics, Jaypee Institute of Information Technology, Noida, India
Department of Mathematics, Jaypee Institute of Information Technology, Noida, India
In this paper, a numerical solution has been developed for hollow circular cylinders made up of orthotropic material which is subjected to twist using micro polar theory. The effect of twisting moment and material internal length on hollow thick-walled circular cylinder made up of micro polar orthotropic material is investigated. Finite difference method has been used to exhibit the influence of shear moduli and material internal length on shear stresses and couple stresses. It is found that the effect of small characteristic length on shear stresses is negligible and couple stresses present its significance when characteristic length is large in solid particle. The behavior of couple stresses are nonlinear for large internal length while for small internal length couple stresses are linear in nature except near the free boundaries. Torsion in hollow cylinder made up of micro polar orthotropic play vital role in the presence of cracks and holes. Therefore, torsional analysis of hollow cylinder plays important role in the field of biomechanics.
http://jsm.iau-arak.ac.ir/article_544407_df304cd933515080b680f2453b0d77d3.pdf
Elastic
Orthotropic
Micro polar
Characteristics length
Twist
Couple stress
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
591
602
544408
Dispersion of Love Wave in a Fiber-Reinforced Medium Lying Over a Heterogeneous Half-Space with Rectangular Irregularity
R.M Prasad
ratanmaniprasad@gmail.com
1
S Kundu
2
Department of Mathematics, S.N. Sinha College, Tekari, Gaya, Bihar-824236, India
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand-826004 ,India
This paper concerned with the dispersion of Love wave in a fiber-reinforced medium lying over a heterogeneous half-space. The heterogeneity is caused by the consideration of quadratic variation in density and directional rigidity of lower half-space. The irregularity has been considered in the form of rectangle at the interface of the fiber-reinforced layer and heterogeneous half-space. The dispersion equation of Love wave has been deduced for existing geometry of the problem under suitable boundary conditions using variable separation method. It has also been observed that for a homogeneous layer with rigidity lying over a regular homogeneous isotropic half-space, the velocity equation coincides with the classical results of Love wave. The effect of the medium characteristics on the dispersion of Love waves has been discussed and the results are displayed with graphs by means of MATLAB programming to clear the physical significance. The study of Love wave dispersion with irregular interface helps civil engineers in building construction, analysis of earthquake in mountain roots, continental margins, and so on. It is also beneficial for the study of seismic waves generated by artificial explosions.
http://jsm.iau-arak.ac.ir/article_544408_baaa77f7856552e7bcd56006fe307ce5.pdf
Fiber reinforcement
Rectangular irregularity
Heterogeneous half-space
Phase velocity
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
603
620
544409
Crack Influences on the Static and Dynamic Characteristic of a Micro-Beam Subjected to Electro Statically Loading
A.R Shahani
shahani@kntu.ac.ir
1
G Rezazadeh
2
A Rahmani
3
Department of Applied Mechanics, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
Mechanical Engineering Departments, Urmia University, Urmia, Iran
Department of Applied Mechanics, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
In the present work the pull-in voltage of a micro cracked cantilever beam subjected to nonlinear electrostatic pressure was studied. Two mathematical models were employed for modeling the problem: a lumped mass model and a classical beam model. The effect of crack in the lumped mass model is the reduction of the effective stiffness of the beam and in the beam model; the crack is modeled as a massless rotational spring the compliance of which is related to the crack depth. Using these two models the pull-in voltage is extracted in the static and dynamic cases. Stability analysis is also accomplished. It has been observed that the pull-in voltage decreases as the crack depth increases and also when the crack approaches the clamped support of the beam. The finding of this research can further be used as a non-destructive test procedure for detecting cracks in micro-beams.
http://jsm.iau-arak.ac.ir/article_544409_2647857eb71ab2ca711671e0112a7050.pdf
MEMS
Cracked micro-beam
Stability analysis
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
621
636
544410
Damping and Frequency Shift in Microscale Modified Couple Stress Thermoelastic Plate Resonators
S Devi
shaloosharma2673@gmail.com
1
R Kumar
rajneesh_kuk@rediffmail.com
2
Department of Mathematics and Statistics, Himachal Pradesh University, Shimla, India
Department of Mathematics, Kurukshetra University, India
In this paper, the vibrations of thin plate in modified couple stress thermoelastic medium by using Kirchhoff- Love plate theory has been investigated. The governing equations of motion and heat conduction equation for Lord Shulman (L-S) [1] theory are written with the help of Kirchhoff- Love plate theory. The thermoelastic damping of micro-beam resonators is analyzed by using the normal mode analysis. The solutions for the free vibrations of plates under clamped-simply supported (CS) and clamped-free (CF) conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for couple stress generalized thermoelastic and coupled thermoelastic plates. A computer algorithm has been constructed to obtain the numerical results. The thermoelastic damping and frequency shift with varying values of length and thickness are shown graphically in the absence and presence of couple stress for (i) clamped-simply supported, (ii) clamped-free boundary conditions. Some particular cases are also presented.
http://jsm.iau-arak.ac.ir/article_544410_3038990ec52988c00f688dc55f94b2ce.pdf
Modified couple stress theory
Thermoelasticity
Thermoelastic damping
Frequency shift
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
637
654
544411
Shear Waves Through Non Planar Interface Between Anisotropic Inhomogeneous and Visco-Elastic Half-Spaces
B Prasad
bishwanathprasad92@gmail.com
1
P Chandra Pal
2
S Kundu
3
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the corrugation. Further, closed form formulae of these coefficients are presented for a corrugated interface of periodic shape (cosine law interface). Numerical computations for this particular type of corrugated interface are performed and a number of graphs are plotted to illustrate the effect of different parameters of the both half-spaces on the reflection and transmission coefficients. It is found that these coefficients depend upon the amplitude of corrugation of the boundary, angle of incidence and frequency of the incident wave and are strongly influenced by the anisotropy, inhomogeneity and visco-elasticity of the half-spaces. Some special cases are also derived.
http://jsm.iau-arak.ac.ir/article_544411_41aa57267a4ef428be2ff2f004d6357e.pdf
SH-waves
Visco-elastic
Inhomogeneity
Anisotropy
Corrugated boundary
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
655
671
544412
Elastic Wave Propagation at Imperfect Boundary of Micropolar Elastic Solid and Fluid Saturated Porous Solid Half-Space
V Kaliraman
vsisaiya@gmail.com
1
R.K Poonia
2
Department of Mathematics, Chaudhary Devi Lal University, Sirsa, Haryana, India
Department of Mathematics, Chandigarh University, Gharuan, Mohali, Punjab, India
This paper deals with the reflection and transmission of elastic waves from imperfect interface separating a micropolar elastic solid half-space and a fluid saturated porous solid half-space. Longitudinal and transverse waves impinge obliquely at the interface. Amplitude ratios of various reflected and transmitted waves are obtained and computed numerically for a specific model and results obtained are depicted graphically with angle of incidence of incident waves. It is found that these amplitude ratios depend on angle of incidence of the incident wave, imperfect boundary and material properties of half-spaces. From the present study, a special case when fluid saturated porous half-space reduces to empty porous solid is also deduced and discussed graphically.
http://jsm.iau-arak.ac.ir/article_544412_4c2fcec010db62e8269d85138925d39a.pdf
Porous solid
Micro polar elastic solid
Reflection
Transmission
Longitudinal wave
Transverse wave
Amplitude ratios
Stiffness
eng
Islamic Azad University Arak Branch
Journal of Solid Mechanics
2008-3505
2008-7683
2018-09-30
10
3
672
687
544413
Free Vibration of Functionally Graded Cylindrical Shell Panel With and Without a Cutout
k.S Sai Ram
sairamks@yahoo.com
1
K Pratyusha
2
P Kiranmayi
3
Department of Civil Engineering RVR&JC College of Engineering Chowdavaram Guntur, India
Department of Civil Engineering RVR&JC College of Engineering Chowdavaram Guntur, India
Department of Civil Engineering RVR&JC College of Engineering Chowdavaram Guntur, India
The free vibration analysis of the functionally graded cylindrical shell panels with and without cutout is carried out using the finite element method based on a higher-order shear deformation theory. A higher-order theory is used to properly account for transverse shear deformation. An eight noded degenerated isoparametric shell element with nine degrees of freedom at each node is considered. The stiffness and mass matrices are derived based on the principle of minimum potential energy. The stiffness and mass matrices of the element are evaluated by performing numerical integration using the Gaussian quadrature. The effect of volume fraction exponent on the fundamental natural frequency of simply supported and clamped functionally graded cylindrical shell panel without a cutout is studied for various aspect ratios and arc-length to thickness ratios. Results are presented for variation of the fundamental natural frequency of the cylindrical shell panel with cutout size for simply supported and clamped boundary conditions.
http://jsm.iau-arak.ac.ir/article_544413_35bccd93828155ccee2f4671534a4598.pdf
Functionally Graded Materials
Free Vibration
Finite Element Method
Higher-order shear deformation theory
Cylindrical shell panel with a cutout