Boundary Condition Effects in Free Vibrations of Higher-Order Soft Sandwich Beams

Natural motions of sandwich beams with a transversely flexible- (soft-) core are analyzed based on a higher-order theory formulation. The theory does not resort to the use of presumed displacement patterns and permits imposition of the different support conditions at the same boundary section. Finite differences are used to approximate the governing equations, and the deflated iterative Arnoldi algorithm is applied to solve the algebraic eigenvalue problem. Free vibration predictions of the higher-order theory are shown to be in good agreement with experiments reported in the literature. The face sheet deflections of the sandwich beams with nonidentical support conditions at the same boundary are different in the close vicinity of that boundary. The interaction between the face sheets and the core plays a crucial role in the vibration response of sandwich beams with a soft core. The parametric study shows that the qualitative sequence of the antisymmetric (global) and symmetric (local) vibration modes varies with face sheet thickness and that there are sandwich beam layouts for which some higher vibration modes arise from the interaction of the basic modes.