Dynamics of Autoparametric Vibration Absorbers Using Multiple Pendulums

Vyas, Ashwin; Bajaj, Anil K.

doi:10.1006/jsvi.2001.3616

Cited by 90 publications

(64 citation statements)

References 16 publications

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“…However, in view of its narrow bandwidth, the LTVA can be ineffective when the primary structure exhibits frequency-energy-dependent nonlinear oscillations. In this context, a nonlinear counterpart to the classical LTVA would be extremely beneficial, and several nonlinear absorbers have been proposed in the literature, see, e.g., [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Experimental Demonstration of a 3D-Printed Nonlinear Tuned Vibration Absorber

Grappasonni

Habib

Detroux

et al. 2016

Nonlinear Dynamics, Volume 1

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Engineering structures are designed to be lighter and more flexible, hence reducing the extent of application of linear dynamic models. Concurrently, vibration mitigation is required for enhancing the performance, comfort or safety in real-life applications. Passive linear vibration absorbers are purpose-built, often designed using Den Hartog's equal-peak strategy. However, nonlinear systems are known to exhibit frequency-energy-dependent oscillations which linear absorbers cannot effectively damp out. In this context, the paper introduces a new nonlinear tuned vibration absorber (NLTVA) whose nonlinear functional form is tailored according to the frequency-energy dependence of the nonlinear primary structure. The NLTVA design aims at ensuring equal peaks in the nonlinear receptance function for an as large as possible range of forcing amplitudes, hence generalizing Den Hartog's method to nonlinear systems. Our focus in this study is on experimental demonstration of the NLTVA performance using a primary structure consisting of a cantilever beam with a geometrically nonlinear component at its free end. The absorber is implemented using a doubly-clamped beam fabricated thanks to 3D printing. The NLTVA performance is also compared with that of the classical linear tuned vibration absorber.

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Section: Introductionmentioning

confidence: 99%

Experimental Demonstration of a 3D-Printed Nonlinear Tuned Vibration Absorber

Grappasonni

Habib

Detroux

et al. 2016

Nonlinear Dynamics, Volume 1

View full text Add to dashboard Cite

show abstract

“…As the excitation frequency is changed, there arise changes in stability in steady-state solution branches either through a pitchfork bifurcation or through a saddlenode bifurcation (turning point). These results are mentioned only for completeness, and typical results for this class of systems, based on averaged equations, can be found in [4] as well as in [12]. For harmonic balance solutions, Floquet multipliers of the system linearized about the periodic orbit may be used to indicate stability.…”

Section: Local Steady-state Periodic Solutionsmentioning

confidence: 99%

“…Banarjee et al [11] studied a system consisting of an n degree-of-freedom (DOF) massspring-damper assembly with a pendulum attached to the kth mass, and investigated periodic solutions and possible bifurcation by using the asymptotic method of averaging. More recently, Vyas and Bajaj [12] again considered a single spring-mass system, but now with multiple pendulums tuned at slightly different frequencies, and showed significant increase in the effective bandwidth of the autoparametric pendulum as a vibration absorber.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of an autoparametric spring–mass–pendulum system

2006

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In this paper, a study of the global dynamics of an autoparametric four degree-of-freedom (DOF) spring-mass-pendulum system with a rigid body mode is presented. Following a modal decoupling procedure, typical approximate periodic solutions are obtained for the autoparametrically coupled modes in 1:2 internal resonance. A novel technique based on forward-time solutions for finite-time Lyapunov exponent is used to establish global convergence and domains of attraction of different solutions. The results are compared to numerically constructed domains of attraction in the plane of initial position and initial velocity for the pendulum. Simulations are also provided for a few interesting cases of interest near critical values of parameters. Results also shed some light on the role played by other modes present in a multi-DOF system in shaping the overall system response.

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“…In [22] , a nonlinear damping element was added in parallel with the LTVA to decrease the maximum LCO amplitude. Other nonlinear vibration absorbers, including the autoparametric vibration absorber [23,24] , the nonlinear energy sink [25−27] and the hysteretic tuned vibration absorber [28] , have also been considered to increase the effectiveness of vibration attenuation.…”

Section: Introductionmentioning

confidence: 99%

Passive Flutter Suppression Using a Nonlinear Tuned Vibration Absorber

Habib

Kerschen

2016

Nonlinear Dynamics, Volume 1

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Limit cycle oscillations (LCOs) occur in many mechanical systems and they are often a source of danger. The addition of a relatively small mass to the host system, attached through a linear spring and a damper (linear tuned vibration absorber, LTVA), significantly improves its stability. The use of a purely nonlinear spring in the absorber (nonlinear energy sink, NES) increases the frequency bandwidth of the absorber, reduce LCO amplitude and avoid subcritical bifurcation at the loss of stability. Recently, a nonlinear tuned vibration absorber (NLTVA) has been proposed, whose restoring force is tailored according to the functional form of the nonlinearity of the primary system. The NLTVA is designed to exploit the positive features of both the LTVA and the NES. In this paper we show that the NLTVA can compensate the detrimental effect of the nonlinearities of the primary system. In other words, the coupled system exhibits a linear-like dynamics, similar to the same system without structural nonlinearities. Considering a Van der Pol -Duffing oscillator as primary system, a closed-form solution for the local compensation of nonlinearities is obtained analytically. Numerical continuation techniques show that the compensation is valid also for large amplitudes of the response.

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Dynamics of Autoparametric Vibration Absorbers Using Multiple Pendulums

Cited by 90 publications

References 16 publications

Experimental Demonstration of a 3D-Printed Nonlinear Tuned Vibration Absorber

Experimental Demonstration of a 3D-Printed Nonlinear Tuned Vibration Absorber

Global dynamics of an autoparametric spring–mass–pendulum system

Passive Flutter Suppression Using a Nonlinear Tuned Vibration Absorber

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