Dynamic Stability of Beams Under Parametric Excitation

Abstract

The present investigation is an attempt to contribute towards the improved understanding of the dynamic stability of beams under parametric excitation. The dynamic stability of ordinary and sandwich beams subjected to longitudinal parametric excitation has been investigated theoretically and experiments have been carried out to validate some of the theoretical findings. The equations of motion have been derived using finite element method. For ordinary beams the instability regions have been established using Floquet’s theory and for sandwich beams modified Hsu’s method proposed by Saito and Otomi has been applied to determine the boundary frequencies of the instability regions. The dynamic stability of a Timoshenko beam with localised damage and having fixed-free, pinned-pinned, fixed-fixed and fixed-pinned boundary conditions has been investigated to study the effects of parameters such as extent of damage, position of damage, static load factor and boundary conditions on its dynamic...