Stiffness matrix method for modeling of guided waves in multilayered anisotropic plates: the dispersion calculator

Abstract

In recent years, research on the modeling of guided waves has made a significant push forward. This is evident by the fact that at least five softwares or code packages have been released since 2018. This is outstanding considering that prior to this date, only the commercial DISPERSE (early 1990s) and the free GUIGUW software (2011) existed. Along with the release of new tools, the computation methods used by these tools have evolved too. While older tools tend to apply traditional root-finding methods such as the Global Matrix Method (GMM, DISPERSE, ElasticMatrix) or the more recent Stiffness Matrix Method (SMM, Dispersion Calculator (DC)), the newer tools tend to rely more on discretizing methods such as the Semi-analytical Finite Element Method (SAFE, SAFEDC), the Spectral Collocation Method (SCM, future version of DISPERSE), and the Spectral Element Method (SEM, GEWtool). The Dispersion Box is notable for the fact that six computation methods can be used: SAFE, GMM, SMM, Hybrid Compliance-Stiffness Matrix Method (HCSMM), Legendre Polynomial Method (LPM), and Fifth Order Shear Deformation Theory (5-SDT). The main reasons for switching to discretizing methods are that these can model waveguides with arbitrary cross sections and that, in case of SCM and SEM, no modal solution can be missed when obtaining dispersion curves. However, SMM as a root-finding method has the advantage that accuracy remains constant at the desired level, whereas in discretizing methods, it depends on the number of sample or collocation points, thereby losing accuracy as the mode shape becomes more complex with increasing frequency. After all, the SMM-implementation in DC has reached a high level of speed and robustness of dispersion curve tracing for guided waves in multilayered anisotropic plates, which allows it to keep up with other tools and computation methods. This is made possible by using mode family specific dispersion equations combined with a robust dispersion curve tracing algorithm. Currently, the numerical model of DC is extended to isotropic rods and pipes. A live demonstration of DC may convince the audience that it is a capable and valuable tool for the community.