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
SN - 1742-6588
VL - 382
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012006
ER -