Sharif Digital Repository

This is the first research on the frequency analysis of a graphene nanoplatelet composite circular microplate in the framework of a numerical-based generalized differential quadrature method. Stresses and strains are obtained using the higher order shear deformation theory. The microstructure is surrounded by a viscoelastic foundation. Rule of the mixture is used to obtain varying mass density and Poisson’s ratio, whereas the module of elasticity is computed by a modified Halpin–Tsai model. Governing equations and boundary conditions of the graphene nanoplatelet composite circular microplate are obtained by implementing Hamilton’s principle. The results show that outer to inner radius ratio... 

In this paper, an analytical solution is presented for free vibration and dynamic behavior of doubly curved laminated shell consisting of a functionally graded core layer and surface attached functionally graded piezoelectric layers. Shell through-thickness kinematics is based on higher order shear deformation theory of shells, whereas a quadratic variation is assumed for electric potential. Using Hamilton's principle and Maxwell's equation, the governing equations of motion under mechanical loads are derived as seven highly coupled partial differential equations. Implementing Laplace transformation, doing few mathematical operations and using Laplace inverse method, time dependencies of... 

In this article an analytical solution is presented for power output from a piezoelectric shallow shell energy harvester using higher order shear deformation theory (HSDT). The energy harvester is made of an elastic substrate layer coupled with one or two surface bonded piezoelectric layers. Mechanical equations of motion with Gauss's equation are derived on the basis of HSDT and solved simultaneously for simply-supported mechanical boundary conditions. The electromechanical frequency response functions that relate the power output and circuit load resistance are identified from the exact solutions. Using Rayleigh damping the influence of structural damping is taken into account. Also... 

In this study, the energy concept along with the first- and third-order shear deformation theories (FSDT and TSDT) are used to predict the large deflection and through the thickness stress of FGM plates. These responses are studied and discussed as a function of plate thickness and the order "n" of a power law function which is considered for the through the thickness variation of the properties of the FGM plate. The results show that the energy method powered by the FSDT and FSDT is capable of predicting the effects of plate thickness on the deformation and the through the thickness stress. Here, also the effects of power "n" on the plate response is clearly depicted. Notably, the... 

In the present study, based on 12-unknown higher order shear deformation theory (HSDT), buckling and vibration analysis of FG-CNTRC rectangular plate are investigated for various types of temperature distribution and boundary conditions. Implementing Hamilton’s principle, the equations of motion are derived and solved by adopting the Navier solution for the simply supported boundary conditions and DQM method for other boundary conditions. Validation is carried out by comparing the numerical results with those obtained in the open literature. Also, a detailed parametric analysis is carried out to illuminate the influence of different system parameters such as CNT distributions, CNT volume... 

This is the first research on the frequency analysis of a graphene nanoplatelet composite circular microplate in the framework of a numerical-based generalized differential quadrature method. Stresses and strains are obtained using the higher order shear deformation theory. The microstructure is surrounded by a viscoelastic foundation. Rule of the mixture is used to obtain varying mass density and Poisson’s ratio, whereas the module of elasticity is computed by a modified Halpin–Tsai model. Governing equations and boundary conditions of the graphene nanoplatelet composite circular microplate are obtained by implementing Hamilton’s principle. The results show that outer to inner radius ratio... 

This is the first research on the free vibration analysis of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic annular plate resting on the visco-Pasternak foundation and subjected to the nonlinear temperature gradient and mechanical loading within the framework of higher-order shear deformation theory (HSDT). Hamilton's principle is employed to establish governing equations within the framework of HSDT. In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Generalized differential quadrature method (GDQM) is applied... 

In this paper the vibration of a spinning cylindrical shell made of functional graded material (FGM) made is investigated. After a brief introduction of FG materials, by employing higher order theory for shell deformation, constitutive relationships are derived. In the next step by utilizing energy method and Hamilton's principle governing deferential equation of spinning cylindrical shell is obtained. By making use of the principle of minimum potential energy, the characteristic equation of natural frequencies is derived. After verification of the results, the effect of changing different parameters such as material grade, L/R, h/R, and spinning velocity on the natural frequency are... 

In the present study, based on 12-unknown higher order shear deformation theory (HSDT), buckling and vibration analysis of FG-CNTRC rectangular plate are investigated for various types of temperature distribution and boundary conditions. Implementing Hamilton’s principle, the equations of motion are derived and solved by adopting the Navier solution for the simply supported boundary conditions and DQM method for other boundary conditions. Validation is carried out by comparing the numerical results with those obtained in the open literature. Also, a detailed parametric analysis is carried out to illuminate the influence of different system parameters such as CNT distributions, CNT volume...