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A method for analyzing the influence of temperature on the dynamic characteristics of structures with viscoelastic dampers is proposed in this paper. Dampers which are described by so-called fractional rheological models are considered. The temperature-frequency superposition principle is used to describe the influence of temperature on the dynamic characteristics. The concept of continuous dependence of damping on an artificially introduced parameter is adopted for solving, in an approximate way, the nonlinear eigenvalue problem from which dynamic characteristics are determined. The correctness and effectiveness of the method was verified by means of two examples. [ABSTRACT FROM AUTHOR]

Highlights: [•] The dynamic characteristics of structures with viscoelastic dampers are determined. [•] The fractional, rheological model of damper is applied. [•] The proposed approach enables the simultaneous use of a few models of damper. [•] The equations of motion are solved using the continuation method. [•] The problem of existence of real eigenvalues is also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Frame structures with viscoelastic dampers mounted on them are considered in this paper. Viscoelastic (VE) dampers are modelled using two, three-parameter, fractional rheological models. The structures are treated as elastic linear systems. The equation of motion of the whole system (structure with dampers) is written in terms of state-space variables. The resulting matrix equation of motion is the fractional differential equation. The proposed state space formulation is new and does not require matrices with huge dimensions. The paper is devoted to determine the dynamic properties of the considered structures. The nonlinear eigenvalue problem is formulated from which the dynamic parameters of the system can be determined. The continuation method is used to solve the nonlinear eigenvalue problem. Moreover, results of typical calculations are presented. [ABSTRACT FROM AUTHOR]

• 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]