Dynamic Stress Concentrations in Infinite Plates with a Circular Cutout Based on Refined Theory

Abstract

In this paper, based on the refined dynamic equations of plate bending vibration, the wave function expansion method is employed to investigate the elastic wave scattering and dynamic stress concentrations in infinite plates with a circular cutout. By applying the orthogonal function expansion method, the problem is reduced into solving a set of infinite algebraic equations. Then, by using the series truncation method, the above infinite algebraic equations reduce to the finite algebraic equations. As examples, the numerical results of dynamic moment concentration factor (DMCF) in infinite plates with one circular cutout under free boundary conditions subjected to an incident flexural wave are presented, and then the influences of the parameters including incident wavenumber, thickness of plates and frequency on the dynamic moment distributions are also analysed. The analyses indicate that the wave type of scattering waves around the circular cutout converts into the propagating wave from the attenuating wave when the cutoff frequency calculated by this study is 0.861 and the DMCFs vary remarkably nearby the cutoff frequency. This phenomenon is more prominent in thick plates.