Mostafa Mirzaei

An analysis is performed in the current investigation to study the vibrations of composite laminated plates integrated with piezoelectric layers. Composite laminated plate is reinforced with graphene platelets (GPLs). Also the amount of GPLs in the layers may be different which results in a piecewise functionally graded (FG) media. Elasticity modulus of the GPLRC media is obtained by means of the Halpin-Tsai rule which contains efficiency parameters to capture the size of reinforcements. First order shear deformation theory of plates and parabolic distribution of electric field through the piezoelectric layers are assumed as the basic assumption. For the piezoelectric layers, both the open circuit and closed circuit conditions are applied. The total strain and kinetic energies of the plate are obtained. After that by means of the general idea of the Ritz method and also Chebyshev polynomials as the basic shape functions, the matrix representation of the equations of motion dealing with free vibration of sandwich plate with piezoelectric face sheets are obtained. Results of this study are first compared with the available data in the open literature. After that novel results are given to explore the effects of different parameters such as the electrical and mechanical boundary conditions, plate geometry, GPL weight fraction and GPL distribution profile. It is shown that with introduction of GPLs, frequencies of the plate may be enhanced for both closed circuit and open circuit conditions.

Current investigation deals with the dynamic response of composite conical panels which are subjected to mechanical shock. It is assumed that composite laminated conical panel is reinforced with graphene platelets (GPLs) where the amount of GPLs may be different in the layers. As a result a piecewise functionally graded media may be achieved. To model the displacement field in the conical panel, Donnell type of kinematic assumptions and also first order shear deformation shell theory are used. To estimate the elasticity modulus of the composite media, Halpin-Tsai rule is applied where the size of Reinforcements is also included. However for Poisson's ratio and mass density the simple rule of mixtures is adopted. The governing motion equations of the panel are established by means of the Ritz method where the shape functions are constructed via the Chebyshev polynomials. Also to trace the displacement field in time domain, Newmark time marching scheme is used. Results of this study are first compared with the available data in the open literature and then novel numerical results are provided to explore the effects of shell geometry, number of layers, GPL weight fraction and GPL patterns. It is shown that deflections of the shell may be alleviated through introduction of GPLs.

An investigation is performed in this research to analyze the free vibration characteristics of carbon nanotube reinforced composite (CNTRC) cylindrical panels with cutout. Distribution of CNTs in the matrix of the composite panel may be uniform or functionally graded. The cylindrical panel has a cutout at the center in a rectangular shape. Following the first-order shear deformation shell theory with the Donnell type of kinematic assumptions, the total kinetic and strain energies of the cylindrical panel are obtained. The eigenvalues problem governing the natural frequencies of the panel is established using the generalized Ritz method where the shape functions are constructed by means of the Chebyshev polynomials. Different boundary conditions such as free, simply supported, shear diaphragm, and clamped may be assumed for the edge of the panel, however, the perforation part of the panel is considered to be free all around. The obtained frequencies are first validated with the simple cases such as CNTRC plates with cutout and CNTRC panels without cutout. Afterwards novel numerical results are provided to analyze the effects of volume fraction of CNT, graded pattern of CNT, boundary conditions, panel geometry, and the hole size. Results of this study show that as the volume fraction of CNTs as reinforcement increases, the natural frequencies of the plate with/without cutout enhance. Also through a proper functionally graded distribution of CNTs as reinforcement the natural frequencies of the panel may be decreased/increased. Communicated by Jie Yang.

In this research, post-buckling response of sandwich beams with carbon nanotube reinforced face sheets subjected to uniform temperature rise loading and resting on a two-parameter elastic foundation is investigated. A single-layer theory formulation based on the first-order shear deformation beam theory is used. Material properties of the media are obtained according to a refined rule of mixtures approach which contains efficiency parameters. Suitable for the large deformations, von-Kármán strains are taken into consideration. The elastic foundation is modelled as the Pasternak model which takes into account the shear interaction of the springs. Material properties of the face sheets are considered to be position and temperature dependent. The governing equations of the system are obtained using the Ritz method for various combinations of clamped, simply supported and sliding supported edges. Post-buckling equilibrium path of the beam is obtained according to an iterative displacement control strategy. Numerical results of the present study are compared with the available data in the open literature. Then, the numerical results are provided to explore the effect of side-to-thickness ratio, volume fraction of carbon nanotube, distribution pattern of carbon nanotube, the ratio of face thickness-to-host thickness, boundary conditions and elastic foundation.