In this paper, we deal with the nonlinear vibration of viscoelastic shell structures. Coupling an approximated harmonic balance method with one mode Galerkin’s procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. To show the applicability and the validity of our approach, the amplitude-frequency and the amplitude loss factor relationships are illustrated for a sandwich plate with a viscoelastic central layer and a viscoelastic circular ring.

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