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

Fotios Georgiades, Jerzy Warminski, Matthew P. Cartmell

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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.
LanguageEnglish
Pages50-60
Number of pages11
JournalMechanics Research Communications
Volume47
DOIs
Publication statusPublished - 2013

Fingerprint

Modal analysis
Torsional stress
Equations of motion
equations of motion
Natural frequencies
inertia
modal response
torsion
resonant frequencies

Cite this

@article{f094b454fbf442018c658677dec0d4fc,
title = "Towards linear modal analysis for an L-shaped beam: equations of motion",
abstract = "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.",
author = "Fotios Georgiades and Jerzy Warminski and Cartmell, {Matthew P.}",
year = "2013",
doi = "10.1016/j.mechrescom.2012.11.005",
language = "English",
volume = "47",
pages = "50--60",
journal = "Mechanics Research Communications",
issn = "0093-6413",

}

Towards linear modal analysis for an L-shaped beam : equations of motion. / Georgiades, Fotios; Warminski, Jerzy; Cartmell, Matthew P.

In: Mechanics Research Communications, Vol. 47, 2013, p. 50-60.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Towards linear modal analysis for an L-shaped beam

T2 - Mechanics Research Communications

AU - Georgiades, Fotios

AU - Warminski, Jerzy

AU - Cartmell, Matthew P.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

U2 - 10.1016/j.mechrescom.2012.11.005

DO - 10.1016/j.mechrescom.2012.11.005

M3 - Article

VL - 47

SP - 50

EP - 60

JO - Mechanics Research Communications

JF - Mechanics Research Communications

SN - 0093-6413

ER -