The principal resonance of a visco_elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied by means of qualitative analysis. The contributions from the visco_elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations were analyzed. The theoretical analysis is verified by numerical results.
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