Application of lumped-mass vibration absorber on the vibration reduction of a nonlinear beam-spring-mass system with internal resonances

Wang, Yi-Ren; Liang, Tzu-Wen

doi:10.1016/j.jsv.2015.04.002

Cited by 13 publications

(8 citation statements)

References 16 publications

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“…(21) contains ξ 0i ξ 0j ξ 0k , an infinite series of nonlinear terms. This hinders the determination of internal resonance with ω 2 ; therefore, we used the method proposed by Van Horssen 6 and followed the procedure described by Wang and Liang 19 to derive the internal resonance conditions created by ω 2 . We first observe the integration term 21, which is the orthogonal product of φ m (x) and…”

Section: Conditions Of Internal Resonance In the Beam System Without Dvamentioning

confidence: 99%

“…The various beam boundary conditions were examined for better understanding the DVA damping effects on beam vibrations. Wang and Liang 19 investigated the damping effects of vibration absorbers with a lumped mass on a hinged-hinged beam. This kind of vibration absorber is able to mitigate vibrations in mechanical or civil engineering structures on an elastic foundation; however, they are not applicable to all suspension systems.…”

Section: Introductionmentioning

confidence: 99%

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Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Wang¹,

Lu²

2017

IJAV

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This study investigated the damping effects of a dynamic vibration absorber (DVA) attached to a hinged-hinged nonlinear Euler-Bernoulli beam. The model constructed in this study was used to simulate suspended nonlinear elastic beam systems or vibrating elastic beam systems on a nonlinear Winkler-type foundation. This makes the modeling in this study applicable to suspension bridges, railway tracks, and even carbon nanotubes. The hinged-hinged beam in this study includes nonlinear stretching effects, which is why we adopted the method of multiple scales (MOMS) to analyze the frequency responses of fixed points in various modes. The use of amplitudes and vibration modes made it possible to examine the internal resonance. Our results indicate that particular elastic foundations or suspension systems can cause 1:3 internal resonance in a beam. The use of 3D maximum amplitude contour plots (3DMACPs) enabled us to obtain a comprehensive understanding of various DVA parameters, including mass, spring coefficient, and the location of DVA on the beam, and thereby combine them for optimal effect. Our results were verified using numerical calculations.

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Section: Conditions Of Internal Resonance In the Beam System Without Dvamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Wang¹,

Lu²

2017

IJAV

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“…The equations contain structural coupling terms and quadratic and cubic nonlinearities due to curvature and inertia. Based on Newton's second law, Euler's angle transformation, and Taylor series expansion, the dimensionless equations of motion of the nonlinear beam can be expressed as follows 11,12,15 (please see Appendix A for details):…”

Section: Isotropic Free-free Beam Modelmentioning

confidence: 99%

“…This section discusses the effects of damping rings on system stability. In equations ( 8), ( 9), (12), and ( 13), the magnitude of wind speed is changed and the Floquet theory is used to analyze the stability of the system. In order to analyze the stability of the system, the perturbation technique is employed.…”

Section: Floquet Theory and Stability Analysismentioning

confidence: 99%

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Vibration reduction and stability analysis of damping rings on nonlinear free-free beam

Wang

Chang

2020

Advances in Mechanical Engineering

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Two damping rings (DRs) are added on a nonlinear free-free elastic beam to reduce vibrations. This elastic beam with free-free boundary conditions can be used to simulate the high speed aircraft fuselage vibrations. Both isotropic beam and compound beam with double-section are investigated. The beam is subjected to a distributed load with the harmonic wind force. The method of multiple scales ((MOMS) a perturbation technique) is employed to analyze this nonlinear problem in frequency domain. DRs with various locations, masses, spring constants, and damping coefficients are analyzed and the maximum amplitude counter plots (MACPs) are compiled to identify DRs’ combinations for the optimal damping effects. The Floquet theory is used to make the basin of attraction (BOA) charts and analyze the stability of the system. This research can be applied in a wide range of engineering problems, such as rocket structures, high-speed aircrafts, satellites, missiles, etc.

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Influence of tuned mass damper on fixed-free 3D nonlinear beam embedded in nonlinear elastic foundation

Wang

2016

Meccanica

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Application of lumped-mass vibration absorber on the vibration reduction of a nonlinear beam-spring-mass system with internal resonances

Cited by 13 publications

References 16 publications

Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Damping Performance of Dynamic Vibration Absorber in Nonlinear Simple Beam with 1:3 Internal Resonance

Vibration reduction and stability analysis of damping rings on nonlinear free-free beam

Influence of tuned mass damper on fixed-free 3D nonlinear beam embedded in nonlinear elastic foundation

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