• Advances in Computational Design
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• v.5 no.1
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Steel and Composite Structures
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• v.33 no.6
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• pp.891-906
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• 2019

This study considers the instability behavior of sandwich plates considering magnetorheological (MR) fluid core and piezoelectric reinforced facesheets. As facesheets at the top and bottom of structure have piezoelectric properties they are subjected to 3D electric field therefore they can be used as actuator and sensor, respectively and in order to control the vibration responses and loss factor of the structure a proportional-derivative (PD) controller is applied. Furthermore, Halpin-Tsai model is used to determine the material properties of facesheets which are reinforced by graphene platelets (GPLs). Moreover, because the core has magnetic property, it is exposed to magnetic field. In addition, Kelvin-Voigt theory is applied to calculate the structural damping of the piezoelectric layers. In order to consider environmental forces applied to structure, the visco-Pasternak model is assumed. In order to consider the mechanical behavior of structure, sinusoidal shear deformation theory (SSDT) is assumed and Hamilton's principle according to piezoelasticity theory is employed to calculate motion equations and these equations are solved based on differential cubature method (DCM) to obtain the vibration and modal loss factor of the structure subsequently. The effect of different factors such as GPLs distribution, dimensions of structure, electro-magnetic field, damping of structure, viscoelastic environment and boundary conditions of the structure on the vibration and loss factor of the system are considered. In order to indicate the accuracy of the obtained results, the results are validated with other published work. It is concluded from results that exposing magnetic field to the MR fluid core has positive effect on the behavior of the system.

• Advances in nano research
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• v.9 no.4
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• pp.237-250
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• 2020

An accurate plate theory for assessing sandwich structures is of interest in order to provide precise results. Hence, this paper develops Layer-Wise (LW) theory for reaching precise results in terms of buckling and vibration behavior of Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) annular nanoplates. Furthermore, for simulating the structure much more realistic, its edges are elastically restrained against in-plane and transverse displacement. The nano structure is integrated with piezoelectric layers. Four distributions of Single-Walled Carbon Nanotubes (SWCNTs) along the thickness direction of the core layer are investigated. The Differential Quadrature Method (DQM) is utilized to solve the motion equations of nano structure subjected to the electric field. The influence of various parameters is depicted on both critical buckling load and frequency of the structure. The accuracy of solution procedure is demonstrated by comparing results with classical edge conditions. The results ascertain that the effects of different distributions of CNTs and their volume fraction are significant on the behavior of the system. Furthermore, the amount of in-plane and transverse spring coefficients plays an important role in the buckling and vibration behavior of the nano-structure and optimization of nano-structure design.