An analytical method for dynamic analysis of systems with viscoelastic dampers has been developed. Some aspects concerning the critical damping of structure with elastically supported viscoelastic damper are discussed. The considered system is governed by the third order differential equation. The one-sided Green's function for deterministic and stochastic cases is derived in closed analytical form. The free vibration and the forced vibration due to half sine impulse loading have been considered. The analytical solution is derived using Green's function and the Laplace transform method. The numerical results are obtained on the basis of MATHEMATICA system. © 2003 Elsevier Ltd. All rights reserved.
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