In this paper, a new viscoelastic size-depended model developed based on a Modified couple stress theory and the for nonlinear viscoelastic material in order to vibration analysis of a viscoelastic nanoplate. The material of the nanoplate is assumed to obey the Leaderman nonlinear constitutive relation and the von Ká rmá n plate theory is employed to model the system. The viscous parts of the classical and nonclassical stress tensors are obtained based on the Leaderman integral and the corresponding work terms are calculated. The viscous work equations are balanced by the terms of size-dependent potential energy, kinetic energy. Then the equations of motion are derived from Hamilton’ s principle. The governing nonlinear integro-differential equations with coupled terms are solved by using the fourth-order Runge-Kutta method and Galerkin approach. The results are validated by carrying out the comparison with existing results in the literature when our model is reduced into an elastic case. In order to explore the vibrational characteristics, the influences of the thickness ratio, relaxation coefficient, and aspect ratio on the frequency and damping ratio were also examined. The results revealed that the frequency, vibration amplitude and damping ratio of viscoelastic nanoplate were significantly influenced by the relaxation coefficient of nanoplate material, and length scale parameter. Also, it was found that with increasing (h/l) the vibration frequency decreases and its amplitude and damping ratio increase.

Microelectromechanical systems (MEMS) are used in many elds of industry like automotive، aerospace and medical instruments. Among the various ways to operate the MEMS devices، the electrostatic actuator is the common mechanism، due to simplicity and fast response. Previous experiments have shown that the mechanical behavior of devices، which their sizes are in order of micron and submicron، are dependent to size dependency. They also have illustrated that by decreasing the dimension of structures، the size dependent e ect is highlighted. In this case، the classical theories are not capable to predict the size dependent e ects and mechanical behavior of the microstructures properly. Therefore، nonclassical theories such as modied couple stress and strain gradient theories have been introduced. It was shown that the modied couple stress theory can accurately predict the size dependent behavior of microstructures. There are some in uences observed in the MEMS، that they have notable e ects on the mechanical behavior of microswitches، such as fringing elds and large de-ection. When the air gap is larger than the electrode's width of microswitches، the impacts of fringing elds and geometric nonlinearity signicantly a ect the mechanical behavior of the system. Therefore، neglecting the abovementioned e ects leads to errors in the instability prediction of microswitches. Most of microswitches consist of a microcantilever with a proof mass and a xed substrate which there is an air gap between them. By applying voltage to the system، the microcantilever starts to de ect into the xed substrate. In this paper، pull-in instability and de ection of MEMS switches are investigated based on the size dependent model. The nonlinear model is introduced by considering modied couple stress theory and fringing eld e ects as well as geometric nonlinearity. Utilizing the minimum total potential energy principle، the static equation of motion is derived in framework of the nonclassical theory. The e ects of various parameters on static pull-in instability are studied and errors of considering the linear model or classical theories is calculated. The results show that the presented model is capable to predict the displacement and pull-in instability of the microswitches.

The main aim is to study the two dimensional axisymmetric problem of thick circular plate in Modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governing equations. The displacements, stress components, temperature change and chemical potential are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of couple stress on the resulting quantities are shown graphically. Some particular cases of interest are also deduced.

In this article, the size effect on the dynamic behavior of a simply supported multi-cracked microbeam is studied based on Modified couple stress theory (MCST). At first, based on MCST, the equivalent torsional stiffness spring for every open edge crack at its location is calculated; in this regard, the stress Intensity Factor (SIF) is also considered for all open edge cracks. Hamilton’ s principle has been used in order to achieve the governing equations of motion of the system and associated boundary conditions are derived based on MCST. Then the natural frequencies of multi-cracked microbeam are analytically determined. After that, the Numerical solutions have been presented for the microbeam with two open edge cracks. Finally, the variation of the first three natural frequencies of the system is investigated versus different values of the depth and the location of two cracks and the material length scale parameter. The obtained results express that the natural frequencies of the system increase by increasing the material length scale parameter and decrease by moving away from the simply supported of the beam and node points, in addition to increasing the number of cracks and cracks depth.

Due to the extensive development and increasing use of microsystems, it is important to predict the behavior of these structures, especially their vibration behavior. In this study, a micro sensor that has been damaged by a crack is investigated. The damaged micro sensor is modeled as a micro beam with a crack. In this modeling, the crack is modeled as a torsion spring. In the modeling, flexoelectric effect, piezoelectric effect, and electric field caused by the applied voltage have been considered. After mathematical modeling, the governing equations have been extracted using Hamilton's principle based on the Modified couple stress theory(MCST). The results of the analytical solution of the equations show that increasing the voltage applied to the micro sensor causes the natural frequency to increase and increasing the piezoelectric constant causes the effective stiffness of the micro structure to increase and as a result the natural frequency increases. Also, the results show that changing the flexoelectric constant in the micro sensor does not significantly change the natural frequency of the system.

Recently, it has been substantiated that besides initially curved micro-structures, pressurized flat micro-plates can also experience snap-through instability. Given the potential applications of these micro-plates in designing high-sensitive sensors, the present work aims to investigate the bi-stable behavior of such structures when they are integrated with a piezoelectric layer. To this end, the Modified couple stress theory together with the geometric nonlinear Kirchhoff plate model are employed. Hiring Galerkin’s method, the reduced governing equilibrium, and stability equations are then achieved. The limit points associated with the micro-plate equilibrium path are then determined through the simultaneous solution of these equations. The present findings are compared and validated by available results in the literature. The influence of the piezoelectric actuation on the bi-stable response of the system is then investigated. The results reveal that the shape of the micro-plate equilibrium path and the number and the position of its limit points can seriously be affected by applying the piezoelectric voltage. Despite the previous studies, the present paper shows that applying positive piezoelectric voltage does not decrease the pull-in threshold of the system all the time and can sometimes increase it when the micro-plate undergoes large differential pressures. Furthermore, the results reveal that applying positive piezoelectric voltages expands the snapping zone while negative ones downsize this region. The present results can be very useful for micro-electromechanical system engineers.

In this paper a N th order nanoplate model is developed for the b ending and buckling analysis of a graphene nanoplate based on a Modified couple stress theory. The strain energy, external work and buckling equations are solved Also using Hamilton’ principle, main and auxiliary equations of nano plate are obtained. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load, the dimensionless critical force under a uni axial surface force in x direction are all obtained for various plate's dimensional ratios and material length scale to thickness ratios. The governing equations are numerically solved. The effect of material length scale, length, width and thickness of the nanoplate on the bending and buckling ratio s are investigated and the results are presented and discussed in details.

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In Modified couple stress theory, the s the sthe sthe strain energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, train energy density is a function of the components strain tensor, curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After curvature tensor, stress and symmetric part of the couple tensor. After obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation obtaining the strain energy, external work, and kinetic energy equation inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in inserting them in the Hamilton principle, main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano the Hamilton principle, main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nanothe Hamilton principle, the main and auxiliary equations of nano-plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in plate are obtained. Then, by applying the boundary and force conditions in governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nano governing equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nanogoverning equations, the vibrations of rectangular Kirschhof nano-plate with plate with plate with plate with plate with plate with plate with the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated the thickness are investigated with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method with simple support around. The solution method used in this study is the Navier methodused in this study is the Navier method used in this study is the Navier methodused in this study is the Navier methodused in this study is the Navier method used in this study is the Navier methodused in this study is the Navier method used in this study is the Navier method used in this study is the Navier method used in this study is the Navier methodused in this study is the Navier methodused in this study is the Navier methodused in this study is the Navier methodused in this study is the Navier method used in this study is the Navier method used in this study is the Navier methodused in this study is the Navier methodused in this study is the Navier method used in this study is the Navier methodused in this study is the Navier method used in this study is the Navier methodused in this study is the Navier methodused in this study is the Navier method used in this study is the Navier methodused in this study is the Navier method andandand the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, the effects of material length scale, length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated length and thickness of the nanoplate on vibration are investigated results are presented and discussed in details results are presented and discussed in details results are presented and discussed in details results are presented and discussed in details results are presented and discussed in details results are presented and discussed in detailsresults are presented and discussed in detailsresults are presented and discussed in details results are presented and discussed in details results are presented and discussed in detailsresults are presented and discussed in details results are presented and discussed in detailsresults are presented and discussed in detailsresults are presented and discussed in detailsresults are presented and discussed in detailsresults are presented and discussed in detailsresults are presented and discussed in detailsresults are presented and discussed in details results are presented and discussed in detailsresults are presented and discussed in details results 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The present study investigates the buckling of a thick sandwich plate under the biaxial non-uniformcompression using the Modified couple stress theory with various boundary conditions. For this purpose, the topand bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials areinvestigated. The simplified first order shear deformation theory (S-FSDT) is employed and the governingdifferential equations are obtained using the Hamilton’ s principle by considering the Von-Karman’ s nonlinearstrains. An analytical approach is applied to obtain exact results with different boundary conditions. Due to the factthat there is no research on the stability of micro/nano sandwich plates based on S-FSDT including the couple stresseffect, the obtained results are compared with the FSDT studies which use the Eringen nonlocal elasticity.