Nonlinear vibration analysis of L-shaped beams and their use in vibration reduction

2022-9
Ekici, Yiğitcan
In this thesis, nonlinear vibration analysis of both fixed L-shaped beam and L-shaped beam attached to a single degree of freedom (SDOF) system is performed for several cases with different structural parameters to observe the effect of these parameters. Then these beams are proposed to reduce the vibration amplitudes of certain structures, and the nonlinear effects on the dynamic responses of these structures are investigated. The nonlinear dynamic model of the L-shaped beam is obtained by using Euler-Bernoulli Beam Theory and Hamilton’s principle. The equations are simplified by disregarding the beams’ axial motions; only the transverse motions are considered in calculations. Galerkin’s method is utilized to discretize the obtained nonlinear partial differential equations into a set of nonlinear ordinary differential equations. These equations are converted into a set of nonlinear algebraic equations using Harmonic Balance Method, which are then solved numerically using Newton’s method with arc length continuation.

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Citation Formats
Y. Ekici, “Nonlinear vibration analysis of L-shaped beams and their use in vibration reduction,” M.S. - Master of Science, Middle East Technical University, 2022.