Towards linear modal analysis for an L-shaped beam: equations of motion

Georgiades, Fotios, Warminski, Jerzy and Cartmell, Mathhew, P. (2013) Towards linear modal analysis for an L-shaped beam: equations of motion. Mechanics Research Communications, 47 . pp. 50-60. ISSN 0093-6413

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We consider an L-shaped beam structure and derive all the equations of motion considering also the rotary inertia terms. We show that the equations are decoupled in two motions, namely the in-plane bending and out-of-plane bending with torsion. In neglecting the rotary inertia terms the torsional equation for the secondary beam is fully decoupled from the other equations for out-of-plane motion. A numerical modal analysis was undertaken for two models of the L-shaped beam, considering two different orientations of the secondary beam, and it was shown that the mode shapes can be grouped into these two motions: in-plane bending and out-of-plane motion. We compared the theoretical natural frequencies of the secondary beam in torsion with finite element results which showed some disagreement, and also it was shown that the torsional mode shapes of the secondary beam are coupled with the other out-of-plane motions. These findings confirm that it is necessary to take rotary inertia terms into account for out-of-plane bending. This work is essential in order to perform accurate linear modal analysis on the L-shaped beam structure.

Additional Information:Published online 28th November 2012
Keywords:L-shaped beam, linear equations of motion, modal analysis, Georgiadis
Subjects:H Engineering > H340 Acoustics and Vibration
H Engineering > H143 Structural Mechanics
H Engineering > H342 Vibration
H Engineering > H300 Mechanical Engineering
H Engineering > H140 Mechanics
H Engineering > H142 Solid Mechanics
H Engineering > H310 Dynamics
H Engineering > H210 Structural Engineering
Divisions:College of Science > School of Engineering
ID Code:9469
Deposited On:16 May 2013 07:48

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