Nonlinear vibration analysis of functionally graded beams

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2022-8
Dedeköy, Demir
In this thesis, nonlinear forced vibrations of functionally graded (FG) Euler-Bernoulli Beams are studied. Two types of nonlinearities, large deformation nonlinearity and nonlinearities resulting from rotating beam dynamics, are considered. The Spectral Chebyshev Technique (SCT) is employed for solving governing equations of the spectral-temporal boundary value problems of beam vibrations, which do not always have closed-form analytical solutions. The SCT is combined with Galerkin’s method to obtain spatially discretized nonlinear differential equations of motion. Those equations of motion are then converted into nonlinear algebraic equations with the Harmonic Balance Method (HBM), which are solved with the help of Newton’s method with arc-length continuation. First, natural frequencies and mode shapes of the uniform and functionally graded beams are obtained with respect to different case scenarios of material distribution properties. A convergence analysis is performed to obtain the minimum number of Chebyshev polynomials required to obtain precise results. Afterward, frequency responses of the nonlinear beams subjected to different boundary conditions are studied.

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Citation Formats
D. Dedeköy, “Nonlinear vibration analysis of functionally graded beams,” M.S. - Master of Science, Middle East Technical University, 2022.