Weight function in a bimaterial strip containing an interfacial crack and an imperfect interface. Application to Bloch-Floquet analysis in a thin inhomogeneous structure with cracks

TL;DR

This paper introduces a weight function for bi-material strips with cracks and uses it to develop an asymptotic algorithm for wave propagation analysis in cracked, inhomogeneous structures.

Contribution

It defines a new weight function for bimaterial strips with cracks and applies it to asymptotic analysis of wave behavior in complex structures.

Findings

Weight function effectively characterizes crack and interface effects.

Asymptotic algorithm accurately predicts wave propagation in cracked structures.

Application to Bloch-Floquet analysis demonstrates practical utility.

Abstract

We define a weight function in a bi-material strip containing a semi-infinite crack and an imperfect interface and analyse a problem of anti-plane shear. We then present an asymptotic algorithm which uses the weight function to evaluate the coefficients in asymptotics of solutions to problems of wave propagation in a thin bi-material strip containing a periodic array of cracks situated at the interface between two materials.