Wave equations in mechanics

Abstract

The classical wave equation is a cornerstone in mathematical physics and mechanics. Its modifications are widely used in order to describe wave phenomena. In mechanics deformation waves are related to impact problems, acoustic waves are used in Nondestructive Evaluation, seismic waves may cause a lot of damage, etc. In this paper it is shown how the classical wave equation can be modified in order to model better the physics of processes. The examples cover microstructured and inhomogeneous materials together with linear and nonlinear models. Beside usual two-wave models, the evolution equations are described which govern the distortion of a single wave.

Analysis of Dynamic Response Behavior of Crack under Impact Stress Wave

“…A stress wave is a state that enters another state at a finite speed and belongs to a type of disturbance wave without giving the medium as a whole any permanent displacement [39,40]. Therefore, waves can occur in media in which energy can be stored in both kinetic and potential forms [11]. The physical process can be better simulated by modifying the classical wave equation.…”

“…Therefore, the propagation of stress waves and the dynamic response behavior of the structure under the impact load has an extremely important influence on the safety and reliability of the components [4][5][6][7][8]. When the metal material is subjected to an external impact load, the wave will propagate outward from the impact area, and the shock wave will pass through the material and cooperate with the boundary [9][10][11][12]. Since the shock stress wave will contain the physical properties and mechanical properties of the metal component materials, the stress wave propagation method is widely used in various engineering fields.…”