A weak-form spectral Chebyshev technique for nonlinear vibrations of rotating functionally graded beams

Date

2023-02-01

Author

Lotfan, Saeed
Dedekoy, Demir
Bediz, Bekir
Ciğeroğlu, Ender

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This study presents the spectral Chebyshev technique (SCT) for nonlinear vibrations of rotating beams based on a weak formulation. In addition to providing a fast-converging and precise solution for linear vibrations of structures with complex geometry, material, and physics, this method is further advanced to be able to analyze the nonlinear vibration behavior of continuous systems. Rotational motion and material gradation further complicate this nonlinear behavior. Accordingly, the beam is considered to be axially functionally graded (FG) and a model representing the forced nonlinear vibrations of the beam about steady-state equilibrium deformations (SSEDs) is developed. The model includes Coriolis, centrifugal softening, and nonlinear stiffening effects caused by coupling of the axial, chordwise, and flapwise motions, and large amplitude deformations. The integral boundary value problem for the rotating structure is discretized using the SCT and element-wise multiplication definition. As a result, mass, damping, and stiffness matrices, as well as internal nonlinear forcing functions and external forcing vectors, are obtained for a given rotating beam. This formulation provides a general representation of nonlinear strain relations in matrix form and circumvents the complexity rising from obtaining and solving the partial differential equations directly. In addition, nonlinear forcing functions are obtained in matrix form which facilitates the application of harmonic balance method easier to obtain the forced nonlinear response.

Subject Keywords

Rotating functionally graded beams, nonlinear vibrations, mode couplings, spectral Chebyshev technique, harmonic balance method, CARBON NANOTUBES, DYNAMIC-ANALYSIS, MODEL, BLADES, STABILITY

URI

https://hdl.handle.net/11511/102672

Journal

MECHANICS OF ADVANCED MATERIALS AND STRUCTURES

DOI

https://doi.org/10.1080/15376494.2023.2181472

Collections

Department of Mechanical Engineering, Article

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Citation Formats

S. Lotfan, D. Dedekoy, B. Bediz, and E. Ciğeroğlu, “A weak-form spectral Chebyshev technique for nonlinear vibrations of rotating functionally graded beams,” MECHANICS OF ADVANCED MATERIALS AND STRUCTURES, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/102672.