An analysis is made of the results obtained in the three-dimensional linearized theory of elastic waves propagating in initially stressed solids. Consideration is given to surface waves along planar and curvilinear boundaries and interfaces, waves in layers and cylinders, waves in composite materials, waves in hydroelastic systems, and dynamic problems for moving loads. The results were obtained in exact formulations.

Elastic waves in bodies with initial (residual) stresses

The effect of pre-stress on the vibration and stability of elastic plates

The possible role of poroelasticity in the apparent viscoelastic behavior of passive cardiac muscle.

An analysis of research available on the problem under consideration shows that at this time: a) Wave propagation in unbounded, bounded, and composite laminar bodies with homogeneous initial states has been studied sufficiently extensively; b) methods to determine the third-order elastic constants have been developed on the basis of existing theories; c) an ultrasonic nondestructive method to determine the stress in solids has been developed, where the stresses averaged over the bulk of the body are determined. In light of the above, in the authors' opinion, the following should be considered the most urgent questions for further investigations on the problem: a) the investigation of wave propagation regularities in bodies with inhomogeneous initial states (it is hence important to execute quantitative and qualitative analyses of the phenomenon); b) development of an ultrasonic nondestructive method of determining the stress in the near surface layers of a solid, which will afford a possibility of determining not only the membrane stresses but also the bending stresses; c) an investigation of the wave propagation regularities in fibrous composites with initial stresses.

Elastic waves in bodies with initial stresses

Stability and vibration of pre-stressed compressible elastic plates

Wave propagation in thin pre-stressed elastic plates

A generalisation of Ko's strain-energy function

The micropolar elastic vibrations of a circular cylinder

The vibrations of a thin-walled elastic cylinder under axial stress

The radial motions of elastic shells

A.J. Willson

Papers

Wave propagation in thin pre-stressed elastic plates

A generalisation of Ko's strain-energy function

The micropolar elastic vibrations of a circular cylinder

The vibrations of a thin-walled elastic cylinder under axial stress

The radial motions of elastic shells