A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports

Abstract

Abstract:In this paper, a modified Fourier solution based on the first-order shear deformation theory is developed for the free vibration problem of moderately thick composite laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports. In this solution approach, regardless of boundary conditions, the displacement and rotation components of the sector plate are written in the form of the trigonometric series expansion in which several auxiliary terms are added to ensure and accelerate the convergence of the series. Each of the unknown coefficients is taken as the generalized coordinate and determined using the RaleighRitz method. The accuracy and reliability of the present solution are validated by the comparison with the results found in the literature, and numerous new results for composite laminated annular sector plates considering various kinds of boundary conditions are presented. Comprehensive studies on the effects of elastic restraint parameters, layout schemes and locations of line/arc supports are also made. New results are obtained for laminated annular sector plates subjected to elastic boundary restraints and arbitrary internal radial line and circumferential arc supports in both directions, and they may serve as benchmark solutions for future researches.

A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges

“…According to the Mindlin plate theory, the transverse displacement of the plate middle surface and the rotations of the cross section, respectively, along the direction and the direction are utilized. Based on the traditional solution method, the admissible functions usually express a Fourier series expansion, because the Fourier functions constitute a complete set and exhibit an excellent numerical stability in the previous study [37][38][39][40][41][42][43]. We found the conventional Fourier series expression to have some defects which contain the convergence problem along the boundary edges except for a few simple boundary conditions, and the derivatives of a Fourier series cannot be obtained simply through term-byterm differentiation.…”

An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner‐Mindlin Rectangular Plate with General Boundary Conditions

“…In addition, the coordinate system ( , , ) is also shown in Figure 1, which will be used in the analysis. The arbitrary boundary technique [43][44][45][46][47] is introduced to implement the general boundary condition in which one group of liner spring ( = 0, , 0, and denote the location of the spring; i.e., 0 represents the location of the edge = 0) and two groups of rotation springs and are introduced to simulate the related boundary forces in each boundary of a plate, as shown in Figure 1. The general boundary condition is easily obtained by assigning the stiffness of the boundary springs with various values.…”