Free Vibration Analysis of an Asymmetric Sandwich Beam Resting on a Variable Pasternak Foundation

The free vibration analysis of a three layered asymmetric sandwich beam resting on a variable Pasternak foundation subjected to a pulsating axial load have been carried out under various boundary conditions by the computational method. A set of Hill's equations has been obtained by the application of extended Hamilton's principle and generalized Galerkin's method. The effects of elastic foundation variation parameter, thickness ratio of two elastic layers, elastic modulus ratio, the ratio of length of the beam to the thickness of the elastic layer, the ratio of the modulus of the shear layer of foundation to the Young's modulus of elastic layer, the ratio of shear modulus of the core to the Young's modulus of the elastic layer, the ratio of the thickness of the Pasternak foundation to the length of the beam and core loss factors on the natural frequency have been studied.