Novel modification to the timoshenko–ehrenfest theory for inhomogeneous and nonuniform beams

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Faculty

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

AIAA Journal

Publication Status

Version of Record

Abstract

Elishakoff et al. once proposed a novel physics-based, low-frequency correction to the Timoshenko–Ehrenfest beam theory. The corrected beam theory is simpler than the classical one because it leads to a single frequency series in the vibrating analysis, without loss of the effect of shear deformation and rotary inertia. In this paper, a further modification is proposed based on Elishakoff’s correction such that the resulting single frequency series fits quite well with the first branch of the Timoshenko–Ehrenfest beam theory up to a relatively high frequency (i.e., the cutoff frequency of Timoshenko–Ehrenfest beams). Most strikingly, the present modification is found to be suitable not only for homogeneous and uniform beams but also for a wide class of beam structures with axial inhomogeneity and/or variable cross section. An inhomogeneous and nonuniform beam with two sharp ends is analytically studied in detail using several different engineering beam models, which fully verifies the necessity and high accuracy of the present modification, particularly for beam structures composed of materials with negative Poisson’s ratio.

First Page

939

Last Page

948

DOI

10.2514/1.J056885

Publication Date

1-1-2020

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