Session: 07-19-01: Symposium on the Anniversary of the Timoshenko-Ehrenfest Beam Model and Other Refined Theories and Vibrations of Continuous Systems

Paper Number: 143599

143599 - Computing Natural Frequencies and Mode Shapes of a Reddy Beam 

This paper presents an algorithm to find natural frequencies and mode shapes of a non-uniform Reddy beam. The algorithm is based on the theory of linear time-varying systems, which has been recently successfully applied to non-uniform Euler-Bernoulli and Timoshenko beams. In this method, spatial state equations are developed. Then, the spatial state transition matrix is computed , which is independent of the boundary conditions of the beam. Then, natural frequencies and mode shape equations are easily derived for any boundary conditions in terms of elements of the state transition matrix evaluated at the right end of the beam. Here, these equations are derived for pinned-pinned and clamped-clamped beams. Numerical results are presented for both uniform and non-uniform beams.

Presenting Author: Alok Sinha The Pennsylvania State University

Presenting Author Biography: Alok Sinha received his Ph.D degree in Mechanical Engineering from Carnegie Mellon University, Pittsburgh, PA. He has been a PSU (Penn State) faculty since August 1983. His areas of teaching and research are Vibration, Control Systems, Jet Engines, Robotics, Neural Engineering and Nanotechnology. He has authored a graduate textbook “Linear Systems: Optimal and Robust Control” , an undergraduate textbook “Vibration of Mechanical Systems” , and a research monograph “Vibration of Nearly Periodic Structures and Mistuned Bladed Rotors”.
He has been associate editors of ASME Journal of Dynamic Systems, Measurement and Control, ASME Journal of Turbomachinery and AIAA Journal. Currently, he serves as an associate editor of Journal of Vibration Engineering and Technologies.
Alok Sinha is a Fellow of ASME, a Fellow of American Association for the Advancement of Science (AAAS) , and an Associate Fellow of AIAA. He has received NASA certificate of recognition for significant contribution to Space Shuttle Microgravity Mission.

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