Slope-inertia model of non-uniform and inhomogeneous Bresse-Timoshenko beams

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Faculty

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

This paper focuses on the free vibration analysis of axially inhomogeneous and nonuniform beams considering the Bresse-Timoshenko slope-inertia model (BTSIM) as the governing equation. The BTSIM governing equation is obtained by modifying the rotational term inthe kinetic energy expression. Tosolve the BTSIM equation analytically, itis reducedto an uncoupled second-order differential equation of Sturm-Liouville type with respecttorotation angle due to bending. This simplified equation is then solved to obtain closed-form solutions for some allowable variation of properties along the beam axis. Natural frequencies are then calculated for different material and geometric nonuniformities along the beam axis, and for various boundary conditions. A comparison between the results obtained for the reduced equation and the finite element methodiscarried out. The original and BTSIM model results are also comparedwithan available experimental result. The effect of changing the kinetic energy expressionisshown by comparing the natural frequencies obtained from the original and BTSIM model for various boundary conditions.

First Page

4158

Last Page

4168

DOI

10.2514/1.J057115

Publication Date

1-1-2018

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