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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]

This study concerns the structural systems in which additional damping was introduced by means of viscoelastic (VE) dampers modeled with the fractional derivative models. The fractional derivative models have an ability to correctly describe the behavior of VE materials in a wide range of frequency, using a small number of model parameters. However, the governing equation of motion includes fractional derivatives together with ordinary ones. In the proposed approach, after applying the Laplace transform and the inverse transform to the equations of motion, the solution obtained for the system with fractional dampers is equivalent to the modal solution used in the case of proportional damping. In order to validate the proposed approach, the maximum response of the structural system equipped with dampers is determined in the time domain. Thus, the equations of motion with fractional derivatives derived for the considered system are numerically integrated. Moreover, the paper extends the response spectrum concept to structures equipped with fractional viscoelastic dampers. [ABSTRACT FROM AUTHOR]

The paper is devoted to non-linear vibrations of plates, made of the Zener viscoelastic material modelled with the Caputo fractional derivative, and in particular to their response to harmonic excitation. The plate geometric non-linearity is of the von Kármán type. In the formulation shear effects and rotary inertia are considered, too. The problem is solved in the frequency domain. A one-harmonic form of the solution for plate displacements corresponding to the plate formulation is assumed. The amplitude equation is obtained from the time averaged principle of virtual work. The time averaging precedes the use of the harmonic balance method. In the space discretization the finite element method is used involving 8-noded rectangular plate elements with selective-reduced integration. Several numerical examples are analyzed and the response curves are found using a path-following method. The purpose of these analyses is to identify material features of the adopted model of viscoelasticity with the fractional derivative. [ABSTRACT FROM AUTHOR]

The problem of non-linear, steady state vibration of beams, harmonically excited by harmonic forces is investigated in the paper. The viscoelastic material of the beams is described using the Zener rheological model with fractional derivatives. The constitutive equation, which contains derivatives of both stress and strain, significantly complicates the solution to the problem. The von Karman theory is applied to take into account geometric nonlinearities. Amplitude equations are obtained using the finite element method together with the harmonic balance method, and solved using the continuation method. The tangent matrix of the amplitude equations is determined in an explicit form. The stability of the steady-state solution is also examined. A parametric study is carried out to determine the influence of viscoelastic properties of the material on the beam's responses. [ABSTRACT FROM AUTHOR]

In paper the design sensitivity analysis of dynamic characteristics of structures with viscoelastic (VE) dampers is considered. The dampers are modeled using the classical rheological model and the rheological model with fractional derivatives. The design sensitivity is analyzed by using direct differentiation method and adjoint variables method. The formulae enabling the calculation of sensitivity of the first and the second order with respect to chosen design parameters have been derived. Sensitivity analysis of eigenvalues, eigenvectors and dynamic characteristics such as natural frequencies and non-dimensional damping ratios are presented. The correctness of the presented formulae is illustrated in examples. [ABSTRACT FROM AUTHOR]

This paper concerns the dynamic analysis of composite beams containing elastic and viscoelastic (VE) layers. A method for determination of the dynamic characteristics of multilayered beams with VE layers (i.e., natural frequencies, non-dimensional damping ratios and modes of vibration) is presented. The Euler-Bernoulli beam theory and the Timoshenko theory are used to describe the elastic and VE layers, respectively. To describe the mechanical properties of a VE layer, the four-parameter rheological model with fractional derivative is applied. A number of particular rheological models are particular cases of this general model. The virtual work principle and the finite element method together with the Laplace transform are used to derive the equation of motion in the frequency domain. The dynamic characteristics of a beam with VE layers are obtained as the solution to a properly defined nonlinear eigenvalue problem. The continuation method is adopted for solving the nonlinear eigenproblem. Several conclusions concerning the accuracy of the method and variability of results are presented on the basis of numerical studies. [ABSTRACT FROM AUTHOR]