M.S. Thesis Presentation by Marie-Blanche Cornil
Tuesday, November 26, 2002

(Dr. Jianmin Qu, advisor)

"Free Vibration of a Beam Subjected to a Large Static Deflection"

Abstract

The problem considered here is the free vibration of a beam that has undergone a large static deflection. The nonlinear equations of motion for the large deflection are derived first. The deflection is then decomposed into static and dynamic parts. The static part is solved analytically and the dynamic part is solved in terms of power series. The coefficients of the unknown series are calculated with a recursive relation. The characteristic equation of the system is determined by the boundary conditions. Natural frequencies and modes of vibration are obtained. These solutions are compared with finite element results to verify their accuracy. Very good agreement is observed. The results are also compared to the natural frequencies of the corresponding naturally curved beam. The influence of the internal stresses due to the large static deflection is crucial in the vibration study.