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.
Highlights
Viscoelastic (VE) materials are often used to build dampers, layers of structural elements and whole structures in order to increase the ability of systems to dissipate more energy, in comparison with conventional ones [1,2]
The examples presented in this chapter have been selected so as to enable the authors to check the correctness of the developed software for frame structures built of VE materials
These considerations are subject to the influence of change in the parameters describing the VE material on the dynamic characteristics of systems
Summary
Viscoelastic (VE) materials are often used to build dampers, layers of structural elements and whole structures in order to increase the ability of systems to dissipate more energy, in comparison with conventional ones [1,2]. The influence of temperature changes on the properties of VE materials is relatively rarely taken into account [10,11,12,13]. In those papers, empirical relationships derived on the basis of experiments were used [10] or the so-called frequency–temperature superposition principle was utilized [12,13]
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