Multi-scale Simulation of Elastic Waves Containing Higher Harmonics

Abstract

Numerical simulation of wave propagation is essential to understand the physical phenomenon of the wide variety of practical problems. However, the requirement of minimum grid point density per wavelength limits the computational stability, convergence, and accuracy of simulation of engineering application by numerical method. The purpose of this paper is to provide an improved framework for simulation of linear and nonlinear elastic wave propagation and guided-wave-based damage identification techniques feasible in the context of online structural health monitoring (SHM). Nonstandard wavelet-based multi-scale operator developed by using finite element discretization is used to represent waves. The proposed masking eliminates the requirement of a very large number of nodes in finite element method necessary for the propagation of such waves. The method is also useful in the situation where higher harmonics of propagating waves are ignored due to very high computational cost. The wavelet-based finite element scheme achieves an excellent numerical simulation and expresses an applicability for the guided waves’ study.