Dynamic instability and free vibration behavior of three-layered soft-cored sandwich beams on nonlinear elastic foundations

The purpose of the present work was to study the dynamic instability of a three-layered, symmetric sandwich beam subjected to a periodic axial load resting on nonlinear elastic foundation. A higher-order theory was used for analysis of sandwich beams with soft core on elastic foundations. In the higher-order theory, the Reddy\'s third-order theory was used for the face sheets and quadratic and cubic functions were assumed for transverse and in-plane displacements of the core, respectively. The elastic foundation was modeled as nonlinear\'s type. The dynamic instability regions and free vibration were investigated for simply supported conditions by Bolotin\'s method. The results showed that the responses of the dynamic instability of the system were influenced by the excitation frequency, the coefficients of foundation, the core thickness, the dynamic and static load factor. Comparison of the present results with the published results in the literature for the special case confirmed the accuracy of the proposed theory.