The problem formulated in this paper is concerned with studies of forced steady-state and natural vibrations of viscoelastic solids. An assessment of the dissipative properties of solids is made using a maximum resonance amplitude for the first case and a minimum rate of vibration decay, determined by analyzing the spectra of complex natural frequencies of viscoelastic solid vibrations, for the second case. Numerical examples are given to demonstrate the efficiency of the present spectrum problem for the optimization of the dissipative properties of constructions.
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