Theoretical Analysis of Transient Waves in a Timoshenko Beam by Ray and Normal Mode Methods
Date Issued
2009
Date
2009
Author(s)
Su, Yu-Chi
Abstract
The topic of dynamics of beams is important in engineering. Among different beam theories, Bernoulli-Euler beam is most widely used owing to simplicity and reasonability. However, for analyzing dynamic problems, the Timoshenko beam is more appropriate.his thesis applies two approaches – ray and normal mode method to deal with the transient response of Timoshenko beam. Ray solution is most accurate and suitable for predicting short time responses and the normal mode method can treat long time responses. Thus, we use the result obtained by ray solution as a standard for the normal mode method to calculate the long time response. Furthermore, the comparison of dynamic and static results is proposed and the frequency responses are discussed as well. On the other hand, the normal mode solution of Bernoulli-Euler beam is demonstrated and we compare its results with Timoshenko beam. The suitable slender ratio of Bernoulli-Euler beam for the analyzing transient displacement response is also presented. In addition, we analyze the responses of the simply supported beam subjected to impact of a steel ball problem. The normal mode solution of the cantilever beam subjected to constant impact force problem is also derived in this study.
Subjects
Timoshenko beam
Bernoulli-Euler beam
normal mode
ray
transient
Type
thesis