Three-dimensional wave propagation and energy flow

Abstract

Realistic mechanical wave propagation problems and acoustic problems in transient dynamics with a broad frequency range require very large systems and many timesteps, to obtain reliable numerical solutions with sufficient high accuracy. New algorithms are to be developed to make effective use of todays hardware features and the visualization of complex prozesses like intensity and energy flow in transient dynamics. The propagation of mechanical waves is characterized by the change and interaction of strain energy and kinetic energy in space and time. A fast explicit FD-algorithm for wave propagation problems and acoustic problems is developed to analyse and visualise the complex behavior of traveling waves. This inherent parallel algorithm is based on the solution of the three-dimensional wave equation as a first order formulation in terms of stresses and velocities or acoustic pressure and particle velocity, representing both forms of energy in a direct way. Because of the small storage required and the short computational time, the algorithm allows numerical investigations of large systems with online graphic simulations to analyse the complex real physical behavior of propagating waves and to make numerical results comparable to measured results. Local mesh refinement helps to minimize numerical errors of the discrete model. Examples of applications are given with dispersional effects of traveling waves, instantaneous intensity distribution and local energy flow of propagating and standing waves. The complex behavior of traveling waves in a bar with a crack is analysed as a three-dimensional system. As a result, a non-destructive testing method is described using impact hammer for the detection, localization and quantification of cracks. The size of the defects can be of some order smaller than the used wave length.