Analysis of dynamic characteristics of viscoelastic frame structures

Abstract

Planar frame structures made of a viscoelastic material are considered in the paper. The technically very important structures made of a homogenous material are contemplated. A family of rheological models (classic and fractional) are used to describe the mechanical properties of the viscoelastic material. In particular, the dynamic characteristics of the structures are of interest. A numerically very efficient method is proposed to determine such characteristics. The method requires the solution to the linear eigenvalue problem for corresponding elastic structures and the solution to a nonlinear, algebraic equation. The presented method is much more efficient than other methods where, very often, the continuation method is used to solve the nonlinear eigenvalue problem. The influence of temperature changes on dynamic characteristics is analyzed using the frequency-temperature principle. The results of several parametric analyses are presented and discussed. For the first time, the influence of temperature on the dynamic characteristics of beams has been studied in detail. Keywords Viscoelastic frame structures • Free vibration • Dynamic characteristics • Ordinary and dynamic finite elements • Influences of temperature

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“…( 22) and substituting into Eq. ( 16), the equation for natural damped frequencies of the viscoelastic beam is obtained [49] x…”

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