Three‐dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling

Abstract

SUMMARYIn this paper, the free vibration analysis of simply-supported and clamped composite laminates, especially thick laminates, is carried out. The three-dimensional theory of elasticity is integrated into a layerwise model via di erential quadrature discretization. All physical governing equations are satisÿed, including the additional constraints of the characteristics of continuity and discontinuity of interfacial transverse and in-plane strains and stresses along the interfaces of composite laminates. E ects of plate aspect and thickness ratios on the free vibration of these laminates are examined in detail. This study demonstrates the applicability, accuracy, and stability of the present methodology, for vibration analyses of composite structures of thick laminated constitution.

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

“…At higher a/h ratios (a/h > 25), the influence on the fundamental frequency is minor. mesh are in good agreement with the 3D laminate solutions of Liew [49] for all values of a/h ratio. It is also observed that the normalized frequencies increase with the increasing of a/h.…”

Free vibration and buckling analysis of composite sandwich plates in thermal environment

“…Since 1958 and the work of Kerwin [3], with the rapid increase of the industrial use of these structures, various structural theories and analysis models proposed for evaluating the characteristics of composite structures have been reviewed and assessed, such as, the classical plate theory, the first-order shear deformation theory (FSDT), the higher order shear deformation theory, layer-wise model, and Zig–zag model [4–9]. In addition, the three-dimensional theory of elasticity also has been carried out for the analysis and study of mechanical behavior of such structures [10,11].…”

An efficient meshfree method for vibration analysis of laminated composite plates

“…the Rizt, p-Ritz and Rayleigh-Ritz methods [5][6][7][8][9][10][11][12][13], the strip element method [14,15], and the discrete singular convolution (DSC) method [16,17]. Bellman et al [18] introduced the differential quadrature technique initially for solving nonlinear partial differential equations, which was later applied to vibration problems of composite laminates [19][20][21][22][23]. Besides, the techniques utilizing the radial basis functions and the RBF-pseudospectral methods for vibration analysis of laminated composite beams and plates have been proposed by Ferreira and his co-workers [24][25][26][27][28][29][30][31].…”