Comparison of non-linear eigensolvers for modal analysis of frequency dependent laminated visco-elastic sandwich plates

Modal analysis of frequency dependent visco-elastic sandwich structures with finite element models leads to a non-linear eigenvalue problem. Many methods have been proposed so far to solve this problem. The present paper compares the asymptotic numerical method to some representative algorithms such as non-linear Arnoldi method, non-linear Jacobi-Davidson method, inverse iteration and iterative shift-invert method. Three mesh refinement levels 1 (~5000 dofs), 2 (~20000 dofs) and 3 (~45000 dofs) have been used. Computational times and accuracy are compared on relevant use cases with frequency dependent visco-elastic materials. Three layered laminated sandwich plates with visco-elastic layers are considered as test cases and two different frequency and temperature dependent materials (ISD112 and PVB) are employed. It is shown that the non-linear Arnoldi method provides the best results in terms of accuracy and CPU time, inverse iteration being the most efficient method for small size problems. Moreover, it is shown that fractional derivative models commonly used to model frequency dependent viscoelastic materials are more CPU intensive than generalized Maxwell models when performing modal analysis of frequency dependent viscoelastic sandwich structures.