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

Fotios Georgiades, Jerzy Warminski, Matthew P. Cartmell

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.
Original languageEnglish
Article number012006
Number of pages6
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 22 Aug 2012


  • L-shaped beam structure
  • differential nonlinear equations
  • rotary inertia


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