Abstract
This paper carries out free and forced vibration analysis of piezoelectric FGM plates resting on two-parameter elastic foundations placed in thermal environments. By employing the third-order shear deformation theory and the finite element method, this work establishes free and forced vibration equations of piezoelectric FGM plates, where the materials are assumed to be varied in the thickness directions, and the mechanical properties depend on the temperature. Then, comparative examples are conducted to verify the proposed theory and mathematical model, and the results of this study and other methods meet a very good agreement. Then, effects of geometrical and material properties such as the feedback coefficient, voltage, volume fraction index, temperature as well as the parameters of elastic foundations on free and forced vibration of the plates are investigated, and the conclusions are given out to provide the effective direction for the design and practical use of these structures.
Highlights
Nowadays, due to the development of science and technology, complicated smart mechanical structures are used more and more in engineering practice, where they are integrated with numerous kinds of materials such as composite materials, functionally graded materials (FGM), piezoelectric layers, magnetorheological materials, and shape memory alloy. erefore, mechanical investigations of these structures need to use advanced approaches and cost much time to deal with
[1] for the first time introduced an isogeometric Bezier finite element (FE) formulation to conduct the static bending and transient analysis of piezoelectric functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs), in which the modified Halpin–Tsai micromechanical model was employed to evaluate the effective mechanical characteristics which varied gradually in the thickness direction of the core layer, and the electric potential was assumed to change linearly through the thickness for each piezoelectric sublayer
Us, one can see that the above studies have only mentioned the mechanical behaviors of FGM beams and plates without piezoelectric layers, and there is no research on the effects of both elastic foundation and temperature, in which the material properties vary with temperature based on the third-order shear deformation theory
Summary
Due to the development of science and technology, complicated smart mechanical structures are used more and more in engineering practice, where they are integrated with numerous kinds of materials such as composite materials, functionally graded materials (FGM), piezoelectric layers, magnetorheological materials, and shape memory alloy. erefore, mechanical investigations of these structures need to use advanced approaches and cost much time to deal with. Hong [26] investigated the free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of the two-parameter elastic foundation using the third-order shear deformation theory of Reddy. Us, one can see that the above studies have only mentioned the mechanical behaviors of FGM beams and plates without piezoelectric layers, and there is no research on the effects of both elastic foundation and temperature, in which the material properties vary with temperature based on the third-order shear deformation theory. This work focuses on free and forced vibration of piezoelectric FGM plates resting on elastic foundations, in which the effect of temperature is taken into account, based on the third-order shear deformation theory and the finite element method, which does not need any shear correction factors.
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