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Sandwich plates as structural members, have received a lot of attention in industrial structures and large construction projects due to their low specific weight, resistance to fatigue and high bending strength. Since Industrial structures are commonly reposed to dynamic loads, plate vibration can result in injury to structures, especially when the excitation frequency is close to the natural frequency of the structure. Therefore, nonlinear vibration analysis of plates is one of the most attended topics in the dynamics of structures. In this article, the nonlinear free vibration of sandwich plates with a viscoelastic core is studied based on von Karman's assumptions and using the First-order shear deformation theory. The viscoelastic properties of the plate core follow Boltzmann's integral law. Also, the Laplace transform is used to convert equations from the time domain to the Laplace domain. For the discretization of the equations, the finite strip numerical method is used. Finally, by numerically solving an eigenvalue problem in the Laplace-Carson domain, the nonlinear frequencies of sandwich plates with a viscoelastic core with different vibration amplitudes are calculated. The results show that, with the increase of the vibration amplitude and the coefficients of the relaxation function of the viscoelastic core, the ratio of the nonlinear frequencies decreases in this type of plates.

This Paper deals with the large amplitude frequency behavior of porous bi-directional functionally graded beams subjected to various boundary conditions which are simply supported, clamped-simply supported, clamped-clamped, and clamped-free utilizing Reddy third-order shear deformation theory and Green’s tensor together with the Von Karman geometric nonlinearity. The material properties of the beam change according to power and exponential law in both directions. The equations of motion and associated boundary conditions are derived by means of Hamilton’s principle. A generalized differential quadrature method in conjunction with a direct numerical iteration method is selected to solve the system of equations. Demonstrating the convergence of this method, the verification is performed by using extracted results from a previous study based on the Timoshenko beam theory. The results of extensive studies are provided to understand the influences of the different gradient indexes, vibration amplitude ratio, porosity coefficient, Tapered ratio, shear and elastic foundation parameters, and boundary conditions on the Large amplitude vibration frequencies of the bi-directional functionally graded beams. The results reveal that non-linear frequencies increase with the rise of elastic foundation and tapered coefficients and the soar of porosities and material gradients in two directions causes a sharp decrease in non-dimensional frequencies. The results of this study, while carefully examining the frequencies of variable cross-sectional functionally graded beams, are effective in the optimal design of bi-directional beams and are very effective in predicting and detecting failure modes of these beams.

The free and forced vibration of rotating FGM beam with piezoelectric layer using first order shear deformation theory and fixed-free boundary condition have been studied in this article. Rayleigh-Ritz method with Chebyshev series are applied to find the natural frequencies. The results showed the natural frequencies are increased as a result of increasing angular velocity or adding piezoelectric layer. More increasing the natural frequencies are caused by applying the voltage on piezoelectric layer or by increasing hub radius. Moreover, the dynamic response of the beam cause by initial conditions is studied. The frequency of the dynamic response was very near to the first natural frequency of the beam. The results had a good agreement with known reference and Abaqus software results. Also, the influence of harmonic, step and impulse force on forced vibration of the beam has been studied. Decreasing the vibration amplitude of the beam is caused by applying angular velocity and piezoelectric voltage.

In this research, the free vibration of a sandwich plate made of smart magnetostrictive face sheets and polymer composite core is studied. The effective elastic properties of carbon nanotube-reinforced composite are obtained by the rule of the mixture and micromechanical approach. A feedback control system follows the magnetization effect of Terfenol-D films on the vibration characteristics of a sandwich plate. Considering velocity feedback control gain value, the dimensionless frequency of sandwich plate can be changed to desired values due to magneto-mechanical coupling in magnetostrictive materials. The equations of motions are derived using Reddy’s third-order shear deformation theory, energy method, and Hamilton’s principle. The differential quadrature method (DQM) as a numerical method is used for calculating the vibration frequency of the sandwich plate. This numerical method presents the optimal results using weighting coefficients. The findings of this study show the effect of the vibration control system and geometrical properties of the composite sheet on vibration frequency of structures. These findings can be used in marine, aerospace, and civil industries.

In this paper, the dynamic stability of a moderately thick rectangular plate carrying an orbiting mass and lying on a visco-elastic foundation is studied. Considering all inertial terms of the moving mass and using plate first-order shear deformation theory, the governing equations on the dynamic behavior of the system are derived. The Galerkin’s method on the basis of trigonometric shape functions is applied to change the coupled governing partial differential equations to a system of ordinary differential equations. Due to the alternative motion of the mass along the circular path over the plate’s surface, the governing equations are the equations with the periodic constant. Applying the semi-analytical incremental harmonic balance method, the influences of the relative thickness of the plate, radius of the motion path, and stiffness and damping of the visco-elastic foundation on the instability conditions of the system are investigated. A good agreement can be observed by comparing the predicted results of the incremental harmonic balance method with the numerical solution results. Based on the findings, increasing the radius of the motion path broadens the instability regions. Moreover, increasing the stiffness and damping of the foundation cause the system more stable.

In this article, an analytical solution for buckling of annular sectorial porous plates, is presented. At first, based on first order shear deformation plate theory, the governing equilibrium equations and boundary conditions are obtained using minimum total potential energy principle. Then, the stability equations of the plate, are derived in terms of infinitesimal displacements using adjacent equilibrium criterion. Since these equations are highly coupled, it is so difficult to find an analytical solution for them. So, by introducing four auxiliary functions and doing some mathematical manipulations, the stability equations are decoupled and converted to two independent differential equation which can be solved analytically. For this purpose, it has been assumed the simply supported boundary conditions for the radial edges and desired boundary conditions for the circumferential edges of the plate. Finally, the critical buckling load has been calculated for different conditions of the plate. In section of numerical results, the effect of different geometrical parameters, such as sector angle, thickness and inner radius of the plate, also effect of porosity of the plate upon the critical buckling load has been studied for different arbitrary boundary conditions on circumferential edges. The result show that the effect of increase in porosity of the plate upon decrease of the critical buckling load is significantly fewer than the effect of geometrical parameters and the boundary conditions.

The present study was aimed at investigating the vibration of composite cylindrical shell filled with internal liquid with simple two-headed boundary conditions. The shell was composed of multilayer composite. First-order shear theory was employed to solve the governing equations of the shell. First loves approximation theory was utilized to write strain-displacement and curvature-displacement equations. Natural frequencies of the composite cylindrical shell filled with fluid were calculated using minimum potential energy principle. The fluid was supposed to be ideal. According to the equations that were obtained through analytical solution, a computerized code was written using MATLAB software in order to achieve an answer for analyzing the vibrations of the shell. In order to make sure about the precision of the results, the composite cylindrical shell was modelled in Abacus Software, and modal analysis was carried out for it. Moreover, the effect of different parameters such as presence of fluid, the density and height of the fluid, the orientation of the fibers, and some geometrical parameters on the natural frequencies of the shell were investigated in empty and filled states of the shell. The transient dynamic response of the composite cylindrical shells filled with internal liquid that was under lateral impulse load was calculated through the principle of mode superposition. Finally, the effect of stable load and motivation frequency on the vibrations of the composite cylindrical shell was examined.

Time depended deformation and critical buckling load of viscoelastic thick plates were studied using finite strip method with the trigonometric functions in longitudinal direction and the polynomial functions in transverse direction. The plates were considered to be thick and the third order shear deformation theory was used to consider the effect of shear stresses in thickness. The mechanical properties of the material were considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. Time history of maximum deflection of viscoelastic plates subjected to transverse loading and unloading on plates was calculated using a fully discretized formulation. In addition, the critical in-plane load of plates was calculated by a nonlinear procedure in different times of loading. Moreover, the effect of thickness and the interaction of biaxial in-plane loading on critical load of plate were studied. The results show that the interaction curves of biaxial critical load of viscoelastic plates have the linear behavior for all time of loading.

The main purpose of this study is to investigate nonlinear buckling analysis of Functionally Graded (FG) cylindrical shells under uniform axial compressive loads by dynamic relaxation (DR) method. The mechanical properties of shell vary continuously throughout the thickness direction according to the power-law، exponential function and the Mori-Tanaka distribution. The poisson’s ratio of the FG cylindrical shell is constant for power-law and exponential function. But in the Mori-Tanaka distribution variations of poisson''s ratio is determined as a function of the thickness direction. The incremental form of nonlinear formulations are based on first order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the equilibrium equations. Some comparison study is carried out to compare the current solution with the results reported in the literature and the ones obtained by the Abaqus finite element software for the isotropic cylindrical shells. Finally، numerical results are presented for critical buckling load with various boundary conditions، grading indices، radius -to- thickness ratio، length -to- radius ratio and variation of poisson’s ratio.

Nonlinear bending of a functionally graded nanocomposite plate reinforced by aligned and straight single-walled carbon nanotubes (SWCNTs) subjected to a uniform transverse load and thermal load is investigated. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction، Four types of distributions of the reinforcement material are considered، that is، uniform and three kinds of functionally graded distributions of carbon nanotubes along the thickness direction of plates. The material properties of SWCNT are determined according to molecular dynamics (MDs)، and then the effective material properties at a point are estimated according to the rule of mixture. The equilibrium equations are based on first-order shear deformation plate theory (FSDT) and von Kármán strains. These system of equations are solved by Dynamic Relaxation method to determine the load-deflection and load-bending moment curves. Some results for nanocomposite plates are compared with the ones reported by the ABAQUS finite element software. Furthermore، some comparison study is carried out to compare the current solution with the results reported in the literature for isotropic and Functionally Graded Materials (FGMs) plates. Numerical results indicate that volume fraction of carbon nanotube، distribution of CNTs، plate width-to-thickness ratio، plate aspect ratio and different boundary condition have pronounced effects on the nonlinear response of nanocomposite plates.

In this paper، magnetic field effect on the free vibration of cylindrical panel made of functionally graded materials resting on pasternak elastic foundation using first order shear deformation theory for simply supported edges is investigated. The governing equations of motion are obtained by using principle of the Hamilton and energy method. These equations are solved by the navier method. The effect of geometrical parameters such as the radius to length ratio، thickness to length ratio، sector angle of cylindrical panel and Pasternak elastic foundation on the natural frequencies are studied. It is observed that the natural frequencies of cylindrical panel made of functionally graded materials with increasing the radius to length ratio، thickness to length ratio، and sector angle of cylindrical panel decreases، while its stability increases by considering the effect of pasternak elastic foundation. Also the natural frequencies of cylindrical panel made of functionally graded materials increases by applied magnetic field and influence of magnetic field on the higher natural frequencies is higher than that of the lower frequencies.

In this study, nonlinear bending analysis of ring-stiffened annular laminated composite plates is studied. A discretely stiffened plate theory for elastic large deflection analysis of uniformly distributed loaded is introduced. The governing equations are derived based on a first-order shear deformation plate theory (FSDT) and large deflection von Karman equations. The numerical results are obtained using the dynamic relaxation (DR) method combined with the central finite difference discretization technique. For this purpose, a FORTRAN computer program is developed to generate the numerical results. In order to verify the accuracy of the present method the results are compared with those available in the literatures and ABAQUS finite element package as well. The computer code can handle symmetric, unsymmetrical and general theta-ply schemes. The effects of the plate thicknesses, different ratio of outer to inner radius, depth of stiffener, boundary condition and laminates lay-up are studied in detail.

The main purpose of this study is to investigate nonlinear bending and buckling analysis of radially functionally graded annular plates subjected to uniform in-plane compressive loads by Dynamic Relaxation method. The mechanical properties of plates assumed to vary continuously along the radial direction by the Mori–Tanaka distribution. The nonlinear formulations are based on first order shear deformation theory (FSDT) and large deflection von Karman equations. The dynamic relaxation (DR) method combined with the finite difference discretization technique is employed to solve the equilibrium equations. Due to the lack of similar research for the bending and buckling of functionally graded annular plates with material variation in the radial direction، some results are compared with the ones obtained by the Abaqus finite element software. Furthermore، some comparison study is carried out to compare the current solution with the results reported in the literature for annular isotropic plates. The achieved good agreements between the results indicate the accuracy of the present numerical method. Finally، numerical results for the maximum displacement and critical buckling load for various boundary conditions، effects of grading index، thickness-to-radius ratio and inner radius -to-outer radius ratio are presented.

Shape memory alloys(SMA) due to the exhibition of certain performance such as high damping, shape memory effects and Super-elasticity are consider for application in engineering systems. In this study, considering the usage of composite-sandwich structures in various industries including aerospace, the effects of SMA parameters such as SMA volume fraction and SMA wires temperature on hybrid sandwich panel free vibrations with transverse flexible core have been surveyed. The SMA wires (NiTiNol) are embedded at the mid-plane of the sandwich face sheets. For analyze, the improved high order theory is applied, First Shear Deformation Theory (FSDT) at the composite face sheets and Elasticity Theory by the assumption of inertia forces at the core. For governing equations of simply support panel Hamiltonian method has been used. At this study it is assumed that the SMA recovery stress produced via temperature actuation is exerted tensely on mid-plane of the face sheets. For solving problem and simplification the Galerkine method is used. The results showed that SMA actuation improves the vibration behaviors of whole sandwich panel.