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• The subspace iteration method is used to solve nonlinear eigenvalue problem. • The continuation method is used to solve the nonlinear Hermitian eigenproblem. • The method presented allows determination of only a part of eigenvalues. • The method was tested for structures with viscoelastic elements. • The models of VE elements are described with the help of fractional derivatives. The paper presents an extension of the subspace iteration method for application in systems with viscoelastic damping elements, which are described by both classical and fractional models. The presented method enables determination of only a certain number of eigenvalues and associated eigenvectors. This is very useful, especially when the considered problem has many degrees of freedom, in which case it would be very time-consuming or even impossible to determine all the eigenvalues. At the same time, from the engineering point of view, it is not necessary to know all the eigenvalues. In this paper, the subspace iteration method is used for the first time to solve the nonlinear eigenproblems which appear in the dynamic analysis of systems with viscoelastic damping elements. The proposed solution consists of assuming the number of eigenvalues to be determined, taking the initial point of iteration and then solving the nonlinear reduced eigenproblem with Hermitian matrices in each iterative loop. The solution to the reduced eigenproblem is obtained using the continuation method, and it is an additional novelty in the paper. The correctness and effectiveness of the proposed approach are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

• The governing equations of the VE Mindlin plates in the Laplace domain are derived • The simple procedure for dynamic characteristics of VE Mindlin plates is proposed. • The simple method to include the temperature influence is included. • Parametric studies of the dynamic characteristics are carried out. This paper is devoted to geometrically linear free vibrations of viscoelastic (VE) Mindlin plates. The governing equations are derived in the Laplace domain. A simple way to take into account the influence of temperature on the damping properties is included using the frequency-temperature superposition principle. The novel approach to the solution of the non-linear problem of free vibrations of VE plates significantly simplifies the procedure reducing it to a linear eigen-value problem and a simple algebraic non-linear equation with one unknown. Several numerical examples involving varying physical parameters of the model are solved and the results are discussed. [ABSTRACT FROM AUTHOR]