Dispersion and attenuation of quasi-Lamb waves in a viscoelastic plate interacting with a confined compressible fluid layer

Abstract

This study examines the dispersion and attenuation characteristics of quasi-Lamb waves in a viscoelastic plate that is in unilateral contact with a compressible, barotropic, inviscid fluid layer, where a rigid boundary constrains fluid motion. The analysis is based on the exact equations of linear viscoelasticity, incorporating Rabotnov’s fractional-exponential operators to model the material’s viscoelastic behavior. The fluid dynamics are described using the linearized Euler equations. By applying appropriate boundary and compatibility conditions, we derive the dispersion equation and obtain analytical expressions for the wave amplitudes. To identify the complex roots of the dispersion equation, we apply an algorithm that minimizes the modulus of the dispersion determinant. Numerical simulations provide dispersion and attenuation curves for different fluid layer thicknesses and various rheological properties of the viscoelastic plate. Although the present study is theoretical, its findings can support experimental analyses in layered fluid–solid systems such as underwater acoustic sensing or biomedical wave propagation. The primary objective is to assess the impact of these rheological parameters and fluid depth on wave propagation characteristics in a system with perfectly bonded, smooth interfaces between the plate and the fluid. Finally, we present conclusions based on numerical findings regarding the role of viscoelastic material properties, fluid depth variations, and the effect of the rigid wall on wave behavior.