### Abstract

Language | English |
---|---|

Pages | 50-60 |

Number of pages | 11 |

Journal | Mechanics Research Communications |

Volume | 47 |

DOIs | |

Publication status | Published - 2013 |

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### Cite this

*Mechanics Research Communications*,

*47*, 50-60. https://doi.org/10.1016/j.mechrescom.2012.11.005

}

*Mechanics Research Communications*, vol. 47, pp. 50-60. https://doi.org/10.1016/j.mechrescom.2012.11.005

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

Research output: Contribution to journal › Article

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 -