In order to describe the rheological behaviour of viscoelastic materials under dynamic loading, the complex modulus representation is used. The present implementation gives the possibility to analyse structures with high damping and to preserve the frequency and temperature dependences for the storage and loss moduli of viscoelastic materials carrying out modelling in the frequency and time domains.

In the method of complex eigenvalues, damped eigenfrequencies and corresponding loss factors are determined from the free vibration analysis. In this case it is necessary to solve the nonlinear generalised eigenvalue problem with the complex frequency dependent stiffness matrix. Solution starts with a constant frequency and at each step the linear generalised eigenvalue problem is solved using the Lanczos method, which is programmed in a truncated version, where the generalised eigenvalue problem is transformed into a standard eigenvalue problem with a reduced order symmetric tridiagonal matrix. In the energy method it is assumed that for structures with slight damping, dynamic characteristics can be calculated by the equation of natural vibrations of the corresponding undamped structure. In this case eigenvalues and corresponding eigenvectors for an elastic structure are determined from the nonlinear generalised eigenvalue problem, but with the real frequency dependent stiffness matrix. This eigenvalue problem is solved like in the previous method, but at each step the subspace iteration algorithm is applied. In the case of harmonic vibrations, the structural frequency response is determined solving the system of complex linear equations using the Gauss algorithm for each frequency. The dynamic characteristics of a structure can be easily obtained from the frequency response function.

The time domain behaviour of viscoelastic structure has been obtained from the frequency domain response by the Fourier transform technique. The proposed method is based on the assumption that any complex input signal can be interpolated by trigonometric polynomials. It is more convenient for this purpose to use the Fourier transform to find the frequency spectra of excitation. The response of a structure for each trigonometric component is calculated exactly using the matrix of transfer functions. Displacements of a structure in the time domain are obtained by the inverse Fourier transform.

Numerical examples are given to demonstrate validity and application of the approaches developed for the free vibration, frequency and transient response analysis of sandwich composite structures with viscoelastic layers. More attention is paid for the analysis of dynamic characteristics obtained using different methods.

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