Analytical Piezoelasticity Solution for Natural Frequencies of Levy-Type Piezolaminated Plates

Abstract

First time, an analytical solution based on three-dimensional (3D) piezoelasticity is developed for the free vibration analysis of Levy-type piezolaminated plates using 3D extended Kantorovich method (EKM). Extended Hamilton principle (which is extended from elastic to piezoelectric case) is further extended to the dynamic version of mixed form containing contributions from the electrical terms. Multi-term multi-field extended Kantorovich method in conjunction with Fourier series (along [Formula: see text]-direction) is employed to obtain two sets of first-order homogeneous ordinary differential equations (8[Formula: see text] along [Formula: see text]- and [Formula: see text]-axes). A robust algorithm is designed (Fortran Code) to extract the natural frequencies and mode shapes of Levy-type piezolaminated plates. The accuracy and efficacy of this technique are verified thoroughly by comparing it with the existing results in the literature and with the 3D finite element (FE) solutions. Numerical results are presented for single-layer piezoelectric and smart sandwich plates considering five different boundary support conditions, three aspect ratios (length to thickness ratio) and electric open and close circuit conditions. The present results shall be used as a benchmark to assess various two-dimensional (2D) and 3D numerical solutions (e.g., FEM, DQM, etc.).

Viscoelastic free vibration analysis of in-plane functionally graded orthotropic plates integrated with piezoelectric sensors: Time-dependent 3D analytical solutions

“…After demonstrating the validation for simply-supported smart piezoelectric plates, the validation is carried out for piezo-laminated smart rectangular plates subjected to arbitrary support conditions. The numerical results obtained from the present power series-based EKM model are compared with the result presented by Susanta and Kumari [93] which are obtained using 3D exact EKM. The numerical results for homogenous (constant) property case are also presented along with graded density and stiffness cases to access the influence of in-plane variation of stiffness and density on the flexural frequencies and electro-mechanical behavior of IPFG plates.…”

“…( 41) into Eq. ( 40), transforms equation (40) to the following form, 42) is a set of 8n first-order coupled ODEs with constant coefficients and this system of ODEs can be solved analytically by following solution approach suggested by Kumari and Behera [93] which is further explained in Appendix D (refer to the supplementary material).…”

“…First, the present results are validated for an orthotropic single-layered piezoelectric rectangular plate subjected to a along the z-direction. Results are compared with the 3D exact result of Heyliger and Saravanos [95], which was obtained by employing the Fourier series approach through which the solution of the ordinary differential equations can be obtained in the exact closed form (therefore, referred as the exact solution approach in literature), and 3D elasticity-based analytical results of Susanata and Kumari [93]. In Table 3, the results are compared for two-type of electrical arrangements, (i) Single-layered PZT-5A plate subjected to closed-circuit (CC) condition at top and bottom surface (ϕ(x, y, ±h/2)=0), (ii) Single-layered PZT-5A plate subjected to Open-circuit (OC) condition at top and bottom surface (D z (x, y, ±h/2)=0).…”