Flutter of a beam in supersonic flow: truncated version of Timoshenko–Ehrenfest equation is sufficient

Author Type

Faculty

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

International Journal of Mechanics and Materials in Design

Publication Status

Version of Record

Abstract

This paper deals with flutter due to gas flow of a uniform and homogeneous beam with shear deformation and rotary inertia effects taken into account. It utilizes the truncated, consistent Timoshenko–Ehrenfest beam model in contrast to the original Timoshenko–Ehrenfest equations. Omission of the fourth order derivative term in the governing differential equation of the original equations of Timoshenko and Ehrenfest is shown to be more consistent than retaining it as is done in the original Timoshenko–Ehrenfest set. The original Timoshenko–Ehrenfest equations are exposed in almost all textbooks published after 1921. However, this paper shows that these original equations are unnecessarily overcomplicated, and simpler set is consistent. This truncation significantly simplifies the analytical and numerical analyses considerably and agrees with the principle of parsimony, i.e. the most acceptable explanation of a phenomenon is the simplest, involving the fewest entities and assumptions. The critical flutter velocities are compared with the results obtained by using the original set of Timoshenko–Ehrenfest equations.

First Page

783

Last Page

799

DOI

10.1007/s10999-021-09537-x

Publication Date

12-1-2021

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