Transformation cloaking and radial approximations for flexural waves in elastic plates

TL;DR

This paper develops a broadband elastic cloak for flexural waves in thin plates, using asymptotic analysis and elastic pre-stress to achieve invisibility around inclusions, addressing the complexity of elastic cloaking.

Contribution

It introduces a novel model for elastic cloaking of flexural waves in plates, including asymptotic derivation and strategies using pre-stress and body forces.

Findings

Successful design of a broadband elastic cloak for flexural waves

Establishment of a rigorous link between the model and wave propagation in thin plates

Discussion of elastic pre-stress as an effective cloaking strategy

Abstract

It is known that design of elastic cloaks is much more challenging than the design idea for acoustic cloaks, cloaks of electromagnetic waves or scalar problems of anti-plane shear. In this paper, we address fully the fourth-order problem and develop a model of a broadband invisibility cloak for channelling flexural waves in thin plates around finite inclusions. We also discuss an option to employ efficiently an elastic pre-stress and body forces to achieve such a result. An asymptotic derivation provides a rigorous link between the model in question and elastic wave propagation in thin solids. This is discussed in detail to show connection with non-symmetric formulations in vector elasticity studied in earlier work.