Free and forced vibrations of an elastically interconnected annular plates system

摘要

Abstract An analytical solution is presented for determining the natural frequencies, mode shapes, and forced responses of a system of elastically connected annular plates with general boundary conditions. By applying the Kirchhoff’s plate theory, the motion of ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} elastically connected plates is described through a set of ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} differential equations. These equations are coupled, thus, hard to solve. A new variable change is presented to uncouple the equations and obtain one decoupled equation for each plate. These equations are solved separately and analytically, and the natural frequencies, mode shapes, and forced responses of the separated plates are obtained. The frequencies of the original system are those calculated analytically for the decoupled system, and the mode shapes and forced responses are obtained by applying the inverse transform. A three plates system with clamped edges is solved to demonstrate this approach. The effects of stiffness coefficients of elastic layers, inner edge radius of the plates, and the frequency of the external harmonic force on the answers are assessed. Applying ABAQUS software, the analytical solution is validated, where a good agreement is observed.