Wave propagation in electro‐magneto‐elastic solid plate of polygonal cross‐sections

Abstract

PurposeThis paper aims to describe the method for solving vibration problem of electro‐magneto‐elastic plate of polygonal (triangle, square, pentagon and hexagon) cross‐sections using Fourier expansion collocation method (FECM).Design/methodology/approachA mathematical model is developed to study the wave propagation in an electro‐magneto‐elastic plate of polygonal cross‐sections using the theory of elasticity. The frequency equations are obtained from the arbitrary cross‐sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the surface of the plate directly. Hence, the FECM is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.FindingsFrom the literature survey, it is clear that the free vibration of electro‐magneto‐elastic plate of polygonal cross‐sections have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of electro‐magneto‐elastic plates are based on the traditional circular cross‐sections only. So, in this paper, the wave propagation in electro‐magneto‐elastic plate of polygonal cross‐sections is studied using the FECM. The computed non‐dimensional frequencies are plotted in the form of dispersion curves and their characteristics are discussed.Originality/valueThe researchers have discussed the circular, rectangular, triangular and square cross‐sectional plates by the boundary conditions. In this problem, the author studied the vibrations of polygonal (triangle, square, pentagon and hexagon) cross‐sectional plates using the geometrical relation which is applicable to all the cross‐sections. The problem may be extended to any kinds of cross‐sections by using the proper geometrical relations.