Elastic Wave Scattering And Dynamic Stress Concentrations Based On The Refined Plate Theory

As a common structure, plates have been widely used in construction, mechanical and aerospace engineering. In the practical application, according to the needs of project design, it is inevitable to open various holes. Due to these holes, the geometric continuity of plates is broken and then the stress concentrations nearby the holes are also produced. The stress concentrations greatly reduce the load carrying capacity of plates and affect the strength and life time of the structure. Thus, the stress concentrations in plates attract the attentions from many scholars at home and abroad.Since the 50s of last century, the investigations on the elastic waves scattering and dynamic stress concentrations have been a hot research topic in the field of mechanics and civil engineering. And it is still in the ascendant in the recent years. These studies greatly promote the development of elastodynamics. Nevertheless, it is not hard to find that the past investigations on the elastic wave scattering and dynamic stress concentrations are mainly based on the plate theory made by various engineering hypotheses. The engineering practice have been proved that these plate theories had some deviations in case of thick plates or high frequency compared with the actual conditions. Meanwhile, these studies are mainly for the infinite plates. As far as the problem of the elastic wave scattering and dynamic stress concentrations in semi-infinite plates with a circular cutout is concerned, it is very difficult to solve because the multiple scatterings and reflections are generated between the plate boundary and the hole. Therefore, the documents in this area are so few.In this paper, based on the refined equations of plate bending vibration, the wave function expansion method and image method are employed to investigate the elastic wave scattering and dynamic stress concentrations in plates with a circular cutout. And the analytical solutions are presented. By applying the orthogonal function expansion method, the boundary value problem is reduced into solving a set of infinite algebraic equations. Subsequently, by adopting the series truncation method, the above infinite algebraic equations are converted into the finite algebraic equations to be calculated. The model coefficients of scattering wave are obtained by satisfying the given boundary condition. Then, the dynamic moment concentration factors are calculated and the numerical simulation is carried out. The work of this paper can be detailed as follow:1. Based on the refined equations of plate bending vibration, wave function expansion method is employed to study the elastic wave scattering and dynamic stress concentrations in infinite plates with a circular cutout. And the analytical solution is obtain. As numerical examples, at different parameters, the dynamic moments distributions around the hole in infinite plates are presented. The influences of the parameters including plate thickness, incident wavenumber of elastic wave, and frequency on the dynamic moment concentration factors around the hole in infinite plates are then analyzed.2. Based on the refined equations of plate bending vibration, wave function expansion method and image method are employed to study the elastic wave scattering and dynamic stress concentrations in semi-infinite plates with a circular cutout. And the analytical solution is obtain. As numerical examples, at different parameters, the dynamic moment distributions around the hole in semi-infinite plates are presented and compared with the results of infinite plates. And the numerical results of the above two kinds of plates are analyzed and investigated. The influences of the parameters including plate thickness, incident wavenumber of elastic wave, distance between the hole and the plate edge, and frequency on the dynamic moment concentration factors around the hole in semi-infinite plates are also discussed.