Transverse vibration analysis of FGM plates with in-plane exponentially non-homogeneous material

Abstract

In this research, free vibration of rectangular functionally graded (FG) plates with in-plane exponentially non-homogeneous material is investigated. Young's modulus and mass density are assumed to vary between a metal-rich and a ceramic-rich zone along one in-plane direction of the plate. The governing differential equation is derived for the case, and a truncated Taylor series expansion technique is utilized to calculate natural frequencies. A Levy-type solution is obtained for plates having two simply supported edges parallel with the material gradient direction. Results for normalized natural frequency are compared with the 4th order Runge-Kutta method, and when possible with exact solution, showing an accurate agreement. Furthermore, a comprehensive parametric study is carried out to determine the effects of different boundary conditions, aspect ratios, and material variations on the free vibration of FGM plates. Nomenclature

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

“…This solution can provide a continuous generalized displacement as well as stress at the interface between PE patches and plate. Moreover, Boreyri et al [468] explored the FV responses of FGM plates with in-plane exponentially nonhomogeneous material. The mass density and E considered to vary along the plate thickness from between a metal-rich and a ceramicrich zone.…”

Free vibration analysis of functionally graded magneto-electro-elastic plates with in-plane material heterogeneity

“…At the same time, other numerical techniques such as the differential quadrature method (Sharma et al, 2012), the meshfree Hermite radial basis collocation technique (Chu et al, 2014), the Chebyshev collocation approach in conjunction with the differential quadrature method (Kumar, 2015), the finite Taylor series expansion approach (Boreyri et al, 2016), the Fourier series combined with the boundary smoothed auxiliary polynomials (Lyu et al, 2017), two dimensional Chebyshev spectral approach (Huang et al, 2019), the pseudo spectral approach (Heshmati and Jalali, 2019), and so on were applied to gain the vibration frequencies and mode shapes of in-plane functionally graded plates under various boundary conditions.…”