The Influence of Boundary Conditions on the Thin Laminate Nonlinear Dynamics With Applications to a Printed Wiring Board

We study the dynamic response of a thin isotropic laminate in nonlinear elasticity with a Von Karman strain field. The equations of motion, in the form of decoupled Duffing equations, are obtained for the deflection of a laminate in the simply supported, rigidly clamped, and loosely clamped boundary conditions. We investigate the laminate modal response with respect to the initial condition, boundary condition, and harmonic forcing. Our numerical computation results revealed the quasi-periodic bifurcation in the nonlinear resonance of the laminate subject to the harmonic excitation. In addition, the laminate chaos presents a sensitive dependence on the initial and loading conditions. Although the thin laminate responses under different boundary conditions are identical to each other, the boundary conditions do affect the resonance deflection and the resonance frequencies subject to the same loading