Free Vibration Analysis of Three Layered Beams with a Soft-Core Using the Transfer Matrix Method

In this study, the free vibration characteristics of symmetric three-layered beams with a soft core, whereby the mass of the core could be ignored, were investigated. The coupling effect of the axial and bending displacements owing to the presence of the soft core was considered. Classical beam theory was employed for analyzing the top and bottom layers, and only the shear deformation was applied for the core layer. The frequency determinant was deduced using the transfer matrix method. The efficacy of the method was demonstrated through a comparison with the natural frequencies obtained in previous studies. To determine the physical phenomena caused by the exchange process in the order of modes of such beams, a new analytical method is proposed. As an example, the dynamic behavior of a three-layered beam was analyzed by examining the changes in the strain energies related to the natural frequencies and mode shapes. All bending-dominated modes were accompanied by the axial displacements because of the existence of a core layer, whereas the axial-dominated modes were uncoupled with the bending displacements. In addition, the efficiency of the proposed method was demonstrated through relevant discussions of the predicted results.