Rayleigh damping for approximating Lamb wave attenuation in finite element simulations

Numerical modeling of Lamb wave propagation is useful in determining sensor placement and other elements of experiment design. A validated numerical model can also help predict the behavior of cases that may be difficult or impossible to measure experimentally. When studying Lamb wave propagation in viscoelastic materials like polymers and polymer composites, an additional consideration of material damping is required. Lamb wave attenuation in the frequency domain can be described using complex material stiffness values. However, the attenuation of Lamb waves in a spatial finite element model must be defined in the spatial domain. In this paper, the feasibility of using Rayleigh damping to model Lamb wave attenuation in finite element simulations is explored. The accuracy of the method is evaluated and the limitations of the model are discussed. Simulations are carried out for a standard polyetherimide (PEI) plate using a finite element model based on previously measured experimental properties. Both fundamental Lamb wave modes (A₀ and S₀) are examined. Additionally, further experimental measurements are conducted over a broader frequency range for the purpose of model improvement. It is found that Rayleigh damping can be used to accurately implement Lamb wave attenuation in time domain finite element simulations over certain frequency ranges of the fundamental modes. It is also found that error is minimized when the rate of attenuation variation with frequency is constant or nearly constant.