Vibration and power flow analysis of periodically reinforced plates

Abstract

In this paper an analytical method is proposed to investigate the vibration and power flows of periodically reinforced plate with general boundary conditions. Both the plate and stiffening beams are modeled as 3D structural components, and the couplings at the interfaces are specified in terms of 3D elastic joints. The displacement function for each stiffening beam is expressed as a modified Fourier cosine series, and the transverse and in-plane displacements for the plate are similarly expressed as the 2D versions of the modified Fourier cosine series expansions. The unknown Fourier coefficients are calculated using the Rayleigh-Ritz technique. The key advantages of the proposed method include: 1) it is capable of dealing with arbitrary boundary and coupling conditions, 2) it allows modeling any number of reinforcing beams with arbitrary lengths, and 3) the structural intensity, power flows, and kinetic energy distributions are readily calculated analytically from the displacement functions through appropriate mathematical (differential) operations, to name a few. The power flow characteristics of periodically reinforced plates are studied against various influencing factors, such as, plate and beam boundary conditions, coupling conditions, excitation locations, and dislocations resulting from minor misplacement of a reinforcing beam. vibrations, reinforced plates, periodic structures, analytical methods Citation:Xu H A, Li W L. Vibration and power flow analysis of periodically reinforced plates.

Analytical Approaches to Vibration Analysis of Thick Plates Subjected to Different Supports, Loadings and Boundary Conditions - A Literature Survey

“…al [66] used Rayleigh-Ritz method and proposed a Fourier series method for the acoustic analysis of rectangular cavity with impedance boundary conditions arbitrarily specified on any of the wall. H.A Xu and W.L.Li [67] used Rayleigh-Ritz technique and proposed analytical method to investigate the vibrations and power flows of periodically reinforced plate with arbitrary boundary conditions. They examined the effect on power flow with change in boundary conditions, excitation locations and coupling conditions by modeling the plate and stiffening beams as 3D structural components, and the couplings at the interfaces in terms of 3D elastic joints.…”