The continuation method for the eigenvalue problem of structures with viscoelastic dampers

• 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.

This paper is concerned with the dynamic analysis of structures with viscoelastic (VE) dampers. A method for determination of the dynamic characteristics of structures with VE dampers is presented. The proposed approach enables the simultaneous use of a few models of VE damper for describing a single structure. To describe the dynamic force deformation characteristics of damper, fractional derivatives are applied. The structure is treated as an elastic linear system but the equations of motion may contain fractional derivatives, in addition to ordinary ones. The dynamic characteristics of a structure with VE dampers are determined as a solution to the appropriately defined eigenvalue problem. The solution to the equations of motion in the frequency domain is given using the continuation method. The problem of existence of real eigenvalues when the fractional model is used is also discussed. Several conclusions concerning the applicability of the proposed method as well as fractional models of VE dampers are formulated on the basis of the results of a numerical analysis.