An Insight on the Estimation of Wave Propagation Constants in an Orthogonal Grid of a Simple Line-Supported Periodic Plate Using a Finite Element Mathematical Model

Abstract

This article describes the propagation of free waves in a two-dimensional periodic plate using the finite element (FE) method. The advantage of periodic structure analysis is that all the dynamic properties of a finite structure are derived from a single phase-frequency curve or surface. Infinite plates are considered as a combination of periodic plates on an orthogonal array of simple, evenly spaced line supports. A single periodic unit of the system is represented by a more accurate high-precision arbitrary triangular shallow shell FE model to find the plane wave frequency in terms of the propagation constants of the 2D periodic plate. Only the purely propagating waves with no attenuation are considered here. The natural frequency of the infinite plate was obtained for different propagation constants in the two directions of the plate. The results are compared with the literature data. The bounding frequency of the propagation surface is compared to the data published from single square and rectangular plates with different edge boundary conditions. In addition, the natural frequency of the plate supported by finite line support with spans Nx (x-direction) and Ny (y-direction) is compared with the frequency obtained from the propagation curve by the discretization principle. The comparison is seen to be very close. It is found that the current PS-FEM approach can be used to generate dispersion relations with reasonable accuracy.