TY - JOUR

T1 - Linear modal analysis of L-shaped beam structures - Parametric studies

AU - Georgiades, Fotios

AU - Warminski, Jerzy

AU - Cartmell, Matthew P.

PY - 2012/8/22

Y1 - 2012/8/22

N2 - Linear modal analysis of L-shaped beam structures indicates that there are two independent motions, these are in-plane bending and out of plane motions including bending and torsion. Natural frequencies of the structure can be determined by finding the roots of two transcendental equations which correspond to in-plane and out-of-plane motions. Due to the complexity of the equations of motion the natural frequencies cannot be determined explicitly. In this article we nondimensionalise the equations of motion in the space and time domains, and then we solve the transcendental equations for selected values of the L-shaped beam parameters in order to determine their natural frequencies. We use a numerical continuation scheme to perform the parametric solutions of the considered transcendental equations. Using plots of the solutions we can determine the natural frequencies for a specific L-shape beam configuration.

AB - Linear modal analysis of L-shaped beam structures indicates that there are two independent motions, these are in-plane bending and out of plane motions including bending and torsion. Natural frequencies of the structure can be determined by finding the roots of two transcendental equations which correspond to in-plane and out-of-plane motions. Due to the complexity of the equations of motion the natural frequencies cannot be determined explicitly. In this article we nondimensionalise the equations of motion in the space and time domains, and then we solve the transcendental equations for selected values of the L-shaped beam parameters in order to determine their natural frequencies. We use a numerical continuation scheme to perform the parametric solutions of the considered transcendental equations. Using plots of the solutions we can determine the natural frequencies for a specific L-shape beam configuration.

KW - L-shaped beam structure

KW - differential nonlinear equations

KW - rotary inertia

UR - http://iopscience.iop.org/article/10.1088/1742-6596/382/1/012006/meta

U2 - 10.1088/1742-6596/382/1/012006

DO - 10.1088/1742-6596/382/1/012006

M3 - Article

VL - 382

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012006

ER -