Radiating and non-radiating sources in elasticity

TL;DR

This paper investigates the inverse source problem in elasticity, showing that nonradiating forces vanish at corners and edges, using the enclosure method and exponential solutions for Navier's equation.

Contribution

It introduces a novel analysis of nonradiating sources in elasticity, revealing their vanishing behavior at geometric singularities, based on new exponential solutions and the enclosure method.

Findings

Nonradiating forces vanish at corners and edges.

Vanishing property extends to transmission eigenfunctions.

New exponential solutions facilitate analysis.

Abstract

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.