Dynamic stability of a pre-twisted, three layered, symmetric sandwich beam

Abstract

Abstract This paper deals with the parametric instability of a pre-twisted, cantilevered, three-layered symmetric sandwich beam subjected to a periodic axial load at the free end. The non-dimensional governing equations of motion and the associated boundary conditions are derived by Hamilton’s principle. These equations are reduced to the time domain by the use of the generalized Galerkin method. This gives rise to a set of coupled Hill’s equations with complex coefficients. The regions of instability are determined by using Hsu’s method, modified for the complex case. The static buckling loads are determined and the influences of the core loss factor and the static load parameter on the system loss factor are investigated. In addition, the effects of pre-twist angle and geometric, shear and static load parameters on the regions of parametric instability are studied.