Nonlinear vibration analysis of uniform and functionally graded beams with spectral Chebyshev technique and harmonic balance method

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Dedeköy, Demir and Ciğeroğlu, Ender and Bediz, Bekir (2023) Nonlinear vibration analysis of uniform and functionally graded beams with spectral Chebyshev technique and harmonic balance method. In: 40th IMAC: A Conference and Exposition on Structural Dynamics, Orlando, FL, USA

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Abstract

In this paper, nonlinear forced vibrations of uniform and functionally graded Euler-Bernoulli Beams with large deformation are studied. Spectral and temporal boundary value problems of beam vibrations do not always have closed-form analytical solutions. As a result, many approximate methods are used to obtain the solution by discretizing the spatial problem. Spectral Chebyshev Technique (SCT) utilizes the Chebyshev Polynomials for spatial discretization and applies Galerkin’s method to obtain boundary conditions and spatially discretized equations of motions. Boundary conditions are imposed using basis recombination into the problem and as a result of this, the solution can be obtained to any linear boundary condition without the need for re-derivation. System matrices are generated with the SCT, and natural frequencies and mode shapes are obtained by eigenvalue problem solution. Harmonic Balance Method (HBM) is used to solve nonlinear equation of motion in frequency domain, with large deformation nonlinearity. As a result, a generic method is constructed to solve nonlinear vibrations of uniform and functionally graded beams in frequency domain, subjected to different boundary conditions.
Item Type: Papers in Conference Proceedings
Uncontrolled Keywords: Nonlinear Vibration, Functionally Graded Beam, Forced Response, Harmonic Balance Method
Subjects: T Technology > TJ Mechanical engineering and machinery > TJ170-179 Mechanics applied to machinery. Dynamics
Divisions: Faculty of Engineering and Natural Sciences > Academic programs > Mechatronics
Faculty of Engineering and Natural Sciences
Depositing User: Bekir Bediz
Date Deposited: 15 Mar 2022 15:33
Last Modified: 11 Sep 2023 10:58
URI: https://research.sabanciuniv.edu/id/eprint/42766

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