Using the gauge condition to simplify the elastodynamic analysis of guided wave propagation

Abstract

In this article, gauge condition in elastodynamics is explored more to revive its potential capability of simplifying wave propagation problems in elastic medium. The inception of gauge condition in elastodynamics happens from the Navier-Lame equations upon application of Helmholtz theorem. In order to solve the elastic wave problems by potential function approach, the gauge condition provides the necessary conditions for the potential functions. The gauge condition may be considered as the superposition of the separate gauge conditions of Lamb waves and shear horizontal (SH) guided waves respectively, and thus, it may be resolved into corresponding gauges of Lamb waves and SH waves. The manipulation and proper choice of the gauge condition does not violate the classical solutions of elastic waves in plates; rather, it simplifies the problems. The gauge condition allows to obtain the analytical solution of complicated problems in a simplified manner.

Keywords

• Elastodynamics
• Navier-Lame equations
• Gauge condition
• Lamb Wave
• SH wave