Forced vibration of beam on Pasternak foundation: A wave evolution analysis

Abstract

This paper concerns wave reflection, transmission, and propagation in beam on Pasternak foundation with wave analysis of vibrations. The advance in a beam placed on a Pasternak foundation and wave propagation method for finite-length beam are respectively reviewed. The matrix relations for beams resting on foundation between the injected waves and externally applied forces and moments are derived. These matrices can be combined with the propagation matrix and the reflection matrices at boundaries to provide a concise and systematic approach to forced vibration analysis of beams resting on foundation subjected to a temporally harmonic force. Two types of the conventional boundary conditions are investigated. Forced response of beams is obtained via sweeping frequency of harmonic force and the wave-train closure principle. From the results, the natural frequencies and mode shapes are calculated. The research in the influence of shear modulus of foundation is provided with illustrations.