Abstract
This paper presents a unified approach to the modelling of elastic solids with embedded dynamic microstructures. General dependences are derived based on Green's kernel formulations. Specifically, we consider systems consisting of a master structure and continuously or discretely distributed oscillators. Several classes of connections between oscillators are studied. We examine how the microstructure affects the dispersion relations and determine the energy distribution between the master structure and microstructures, including the vibration shield phenomenon. Special attention is given to the comparative analysis of discrete and continuous distributions of the oscillators, and to the effects of non-locality and trapped vibrations.This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.
Highlights
In contrast to solid-state physics, where crystalline solids and periodically structured media are considered as a standard framework, the preference in solid mechanics is given to continuous models
This paper has presented a unified approach to the analytical description of the role of discrete and continuous dynamic microstructure embedded into an elastic body
The use of lattice Green’s functions leads to the modelling of waves in structured high-contrast waveguides with an emphasis on space and time non-locality
Summary
In contrast to solid-state physics, where crystalline solids and periodically structured media are considered as a standard framework, the preference in solid mechanics is given to continuous models. For waves in a system with continuously and discretely distributed oscillators, we evaluate the ratio of wave amplitudes in the master structure and in the embedded substructure It appears that the amplitude in the master system tends to zero as the wave frequency approaches the band gap boundary. We consider a symmetric spherical wave in a homogeneous isotropic structured composition, where the microstructure is represented by a micro-oscillating medium using homogeneously distributed oscillators. In this case, there are no external forces, p1 = p2 = 0, and ψ = 0.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
