Transient and periodic shear wave propagation in a solid-fluid coupled system

TL;DR

This paper analyzes how shear waves propagate and dissipate in a coupled solid-fluid system under sinusoidal forcing, combining analytical series solutions with numerical simulations to explore transient and steady-state behaviors.

Contribution

It provides a novel analytical series solution for shear wave propagation in a coupled solid-fluid system and investigates its transient and steady-state dynamics.

Findings

Transient elastic waves reflect within the solid layer.

Viscous dissipation occurs in the fluid layer.

System behavior varies from damped oscillation to resonant response.

Abstract

A coupled system composed of a Newtonian fluid located on a sinusoidally-forced elastic solid is studied analytically and numerically. The focus is on the transient evolution from the beginning of the forced oscillations and on the periodic behaviour established once the transient has vanished. The analytical solution is expressed as series summations that elucidate the propagation and reflections of elastic transverse waves through the solid layer and the viscous dissipation of oscillations in the fluid layer. Short-term transients in both the fluid and the solid form at every interaction between an elastic wave and a solid boundary. The long-term transient, quantified by the power balance in the fluid layer, instead pertains to the formation of all the elastic waves in the solid layer. The system can be viewed as a generalised transient Stokes layer generated by the elastic waves or as a damped resonant oscillator when the velocity at the fluid-solid interface increases significantly with respect to the forcing amplitude. A parametric study is carried out for three applications of technological interest, i.e. the indirect measurement of fluid viscosity, the turbulent drag reduction by travelling shear waves and the sensing and manipulation of biological flows.