Nonlinear resonances of axially functionally graded beams rotating with varying speed including Coriolis effects

Date

2021-11-01

Author

Lotfan, Saeed
Anamagh, Mirmeysam Rafiei
Bediz, Bekir
Ciğeroğlu, Ender

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

279
views

0
downloads

The purpose of the current study was to develop an accurate model to investigate the nonlinear resonances in an axially functionally graded beam rotating with time-dependent speed. To this end, two important features including stiffening and Coriolis effects are modeled based on nonlinear strain relations. Equations governing the axial, chordwise, and flapwise deformations about the determined steady-state equilibrium position are obtained, and the rotating speed variation is considered as a periodic disturbance about this equilibrium condition. Multi-mode discretization of the equations is performed via the spectral Chebyshev approach and the method of multiple scales for gyroscopic systems is employed to study the nonlinear behavior. After determining the required polynomial number based on convergence analysis, results obtained are verified by comparing to those found in literature and numerical simulations. Moreover, the model is validated based on simulations carried out by commercial finite element software. Properties of the functionally graded material and the values of average rotating speed leading to 2:1 internal resonance in the system are found. Time and steady-state responses of the system under primary and parametric resonances caused by the time-dependent rotating speed are investigated when the system is tuned to 2:1 internal resonance. A comprehensive study on the time response, frequency response, and stability behavior shows that the rotating axially functionally graded beam exhibits a complicated nonlinear behavior under the effect of the rotating speed fluctuation frequency, damping coefficient, and properties of the functionally graded material.

Subject Keywords

Rotating beam, Functionally graded material, Parametric resonance, Primary resonance, Gyroscopic system, Nonlinear vibrations, FREE-VIBRATION ANALYSIS, SPECTRAL-TCHEBYCHEV SOLUTION, DYNAMIC-ANALYSIS, CANTILEVER BEAM, MODEL, BLADE, SATURATION, STABILITY, BEHAVIOR, SYSTEM

URI

https://hdl.handle.net/11511/94863

Journal

NONLINEAR DYNAMICS

DOI

https://doi.org/10.1007/s11071-021-07055-1

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

Nonlinear Vibration Analysis of Uniform and Functionally Graded Beams with Spectral Chebyshev Technique and Harmonic Balance Method Dedekoy, Demir; Ciğeroğlu, Ender; Bediz, Bekir (2023-01-01) 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 condi...
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...
Nonlinear 3D Modeling and Vibration Analysis of Horizontal Drum Type Washing Machines Baykal, Cem; Ciğeroğlu, Ender; Yazıcıoğlu, Yiğit (2020-01-01) In this study, a nonlinear 3-D mathematical model for horizontal drum type washing machines is developed considering rotating unbalance type excitation. Nonlinear differential equations of motion are converted into a set of nonlinear algebraic equations by using Harmonic Balance Method (HBM). The resulting nonlinear algebraic equations are solved by using Newton’s method with arc-length continuation. Several case studies are performed in order to observe the effects of orientation angles of springs and damp...
Nonlinear vibration analysis of L-shaped beams and their use in vibration reduction Ekici, Yiğitcan; Ciğeroğlu, Ender; Yazıcıoğlu, Yiğit; Department of Mechanical Engineering (2022-9) 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-Bern...
Nonlinear Vibrations of a Beam with a Breathing Edge Crack Batihan, Ali C.; Ciğeroğlu, Ender (2015-02-05) In this paper, nonlinear transverse vibration analysis of a beam with a single edge crack is studied. In literature, edge cracks are generally modeled as open cracks, in which the beam is separated into two pieces at the crack location and these pieces are connected to each other with a rotational spring to represent the effect of crack. The open edge crack model is a widely used assumption; however, it does not consider the nonlinear behavior due to opening and closing of the crack region. In this paper, a...

Citation Formats

S. Lotfan, M. R. Anamagh, B. Bediz, and E. Ciğeroğlu, “Nonlinear resonances of axially functionally graded beams rotating with varying speed including Coriolis effects,” NONLINEAR DYNAMICS, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94863.