An improved Fourier series solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions

Abstract

In this article, the authors presented a unified solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. Regardless of the shapes of the plates and the types of boundary conditions, each displacement and rotation component of the elements is expanded as an improved Fourier series expansion which is composed of a double Fourier cosine series and several auxiliary functions introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations. Since the displacement fields are constructed adequately smooth throughout the entire solution domain, an exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the plates. The accuracy, reliability, and versatility of the current solution is fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. Some new results of free vibration analysis for composite laminated annular sector plate, circular sector plate, annular plate, and circular plate are presented, which may be served as benchmark solution for future computational methods. The effects of the sector angles, layer numbers, and boundary spring stiffness on vibration characteristics of the plates are reported. In addition, the force vibration analysis of the plates is also studied. The influence of the boundary spring stiffness, layer number, orthotropic stiffness ration, and fiber orientation angle on dynamic characteristics of the plates is investigated.

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

“…There have been a lot of references about the RayleighRitz technology, such as [60][61][62], and Ritz like methods, such as [63][64][65]. In this paper, based on the Rayleigh-Ritz technology, a set of linear algebraic equations directed against Fourier unknown coefficients on displacement equations can be got by combining (18)-(23e) simultaneously.…”

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

“…Q k ij (i,j =1, 2, 4-6) are the lamina stiffness coefficients [56], which are found from following equations:…”

New Frequency‐Dependent Trigonometric Interpolation Functions for the Dynamic Finite Element Analysis of Thin Rectangular Plates

“…Thus, it is a method that is only applicable to a few very simple boundary conditions. In the Improved Fourier Series Method (IFSM), modifications have been made to eliminate all of the discontinuities and accelerate convergence [5]. It has also made this method applicable to many plate types and boundary conditions; however, even with the modifications IFSM still remains an analytical method that falls short in adaptability when applied to study the vibration behaviour of complex, real-life structural configurations that could be approximated as thin plates or thin plate assemblies.…”