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

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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Samandari, Hamed; Ciğeroğlu, Ender (2015-02-05)
Flexible L-shaped beams are integrated sub-components of several navy and space structures where overall response of the system is affected by these structures. Hence, an understanding of the dynamical properties of these structural systems is required for their design and control. Recent studies show that the dynamic response of beam like structures undergoing large deformation is nonlinear in nature where phenomenon such as jump and chaotic response can be detected. In this study, nonlinear free vibratio...
Nonlinear system identification and nonlinear experimental modal analysis by using response controlled stepped sine testing
Karaağaçlı, Taylan; Özgüven, Hasan Nevzat; Department of Mechanical Engineering (2020-12-24)
In this work, two novel nonlinear system identification methods are proposed in both the modal and spatial domains, respectively, based on response-controlled stepped-sine testing (RCT) where the displacement amplitude of the excitation point is kept constant throughout the frequency sweep. The proposed nonlinear modal identification method, which is also a nonlinear experimental modal analysis technique, applies to systems with several nonlinearities at different (and even unknown) locations (e.g. joint no...
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.