A comparative study for calculating dispersion curves in viscoelastic multi-layered plates

This study examines and critically compares various commonly used models for calculating complex wavenumbers in viscoelastic orthotropic multi-layer materials (e.g. fiber reinforced polymer laminates). Both exact 3D elasticity theory based methods and approximate methods are considered for wave propagation analysis: (i) global matrix method (GMM), (ii) stiffness matrix method (SMM), (iii) hybrid compliance-stiffness matrix method (HCSMM), (iv) semi analytical finite element (SAFE) method, (v) Legendre polynomial method (LPM), and (vi) fifth order shear deformation theory (5-SDT). A detailed mathematical formulation is provided for each of these techniques.The accuracy and the computational efficiency for calculating complex wavenumbers over a wide frequency range are analyzed for both homogenized and multi-layered viscoelastic orthotropic media. This information is helpful to select the proper method to be used in inversion schemes for material characterization. A comparative analysis is also performed on the computed through thickness displacement fields within the solid medium. The different implemented methods have been compiled in a toolbox with a graphical user interface, called The Dispersion Box, and can be freely downloaded from Orta et al. (2022).

Automated summary

This study critically compares various commonly used models for calculating complex wavenumbers in viscoelastic orthotropic multi-layer materials. The accuracy and computational efficiency of these models are analyzed for material characterization. A comparative analysis is also performed on the through thickness displacement fields in the solid medium.