Parametric instability of a cross-ply laminated beam with viscoelastic properties under a periodic force

The parametric instability of a laminated beam subjected to a periodic loading is studied taking viscoelastic properties of the material into account. The governing equations are derived from Hamiltonʹs principle with Boltzmannʹs superposition principle for linear viscoelastic constitutive equation. Applying the finite element method, stability boundaries are determined by means of the method of multiple scales. The stabilizing effect of viscoelasticity of the material on the primary resonance or combination resonance of a parametrically excited system is shown