DYNAMIC STABILITY OF BEAMS ON PASTERNAK FOUNDATION UNDER TIME-VARYING AXIAL LOADS

This paper investigates the dynamic stability of structures subjected to periodic loads, modeled as beams on a Pasternak foundation experiencing time-varying compressive forces. The stability analysis is conducted using the Euler-Bernoulli beam theory, the Mathieu-Hill equations, and the Floquet theory. The results indicate that variations in the foundation’s stiffness and shear modulus significantly influence stability regions, especially at higher frequencies. Stiffness has a more pronounced effect, reducing the unstable region, while changes in both parameters affect the minimum excitation intensity required to induce instability. These findings highlight complex interactions between stiffness and shear properties, suggesting the need for further investigation.