Comparison of several numerical methods for mechanical systems with impacts

Janin, O.; Lamarque, Claude‐Henri

doi:10.1002/nme.206

Cited by 26 publications

(16 citation statements)

References 35 publications

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“…As a result, the primary system attains smaller displacement amplitude than that in the situation without impacts. For the modeling of impact damper on a vibratory system, it is necessary to derive lot of formulas for the steady-state response with two symmetric impacts per cycle or arbitrary number of impacts under sinusoidal excitation (Barbara, 2001;Janin and Lamarque, 2001;Yao et al, 2005). At present, most of the dynamic characteristic investigations of impact dampers assume that the impact condition between the impact damper and the primary system is governed by the coefficient of restitution, which results in discontinuity in the phase plane.…”

Section: Introductionmentioning

confidence: 99%

Inner mass impact damper for attenuating structure vibration

Jian

2006

International Journal of Solids and Structures

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The behaviors of a vibration system suppressed with an impact damper are investigated, where the impact damper is simplified as a combination of spring and viscous damping. The analytical theory for the optimal impact control algorithms for impact damper is developed, and the accurate expressions are derived for the optimal values of the impact damper damping and initial displacement in a single-degree-of-freedom structure. The relation between coefficient of restitution and impact damping ratio is obtained. The investigation shows that the effective reduction of the vibration response is nearly independent of the number of impacts, but primarily related to the type of collision which the impact mass collides with the main mass face-to-face. This theory is generalized to continuous structures. An example of an impact damper in a rotating cantilever beam demonstrates that the impact dampers are suitable for attenuating the impulse response of structures unconditional stable without the requirement of the accuracy of the modal information.

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Section: Introductionmentioning

confidence: 99%

Inner mass impact damper for attenuating structure vibration

Jian

2006

International Journal of Solids and Structures

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“…As a quick aside, let us briefly comment on the affects of the aforementioned partial timestepping and root finding on the accuracy of event‐driven simulations. In , it is proven, for the specific case of an oscillator subject to a linear unilateral constraint, that the root finding to determine a collision time τ must be at least O ( h 4 ) to preserve the fourth‐order accuracy of a given discrete flow map when handling the nonsmooth case. Analysis of our more general nonsmooth systems, in which the unilateral constraint is a nonlinear function ϕ ( q ), is significantly more complex.…”

Section: Structured Integration Methods For Impactsmentioning

confidence: 99%

Discrete Lagrangian mechanics for nonseparable nonsmooth systems

Pekarek¹,

Murphey²

2015

Numerical Meth Engineering

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Summary We consider event‐driven schemes for the simulation of nonseparable mechanical systems subject to holonomic unilateral constraints. Systems are modeled in discrete time using variational integrator (VI) theory, by which equations of motion follow from discrete variational principles. For smooth dynamics, VIs are known to exactly conserve a discrete symplectic form and a modified Hamiltonian function. The latter of these conservation laws can play a pivotal role in stabilizing the energy behavior of collision simulations. Previous efforts to leverage modified Hamiltonian conservation have been limited to integrators using the Störmer–Verlet method on separable, nonsmooth Hamiltonian mechanical systems. We generalize the existing approach to the family of all VIs applied to nonseparable, potentially nonconservative Lagrangian mechanical systems. We examine the properties of the resulting integrators relative to other structured collision simulation methods in terms of conserved quantities, trajectory errors as a function of initial condition, and required computation time. Interestingly, we find that the modified collision Verlet algorithm (MCVA) using the Störmer–Verlet integrator defined as a composition method leads to the best accuracy. Although relative to this method, the VI‐based generalized MCVA method offers computational savings when collisions are particularly sparse. Copyright © 2015 John Wiley & Sons, Ltd.

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“…The first developments have been pioneered by Jean and Moreau, see e.g. (Jean, 1999;Jean and Moreau, 1987), continued by numerous investigations (Doyen et al, 2011;Janin and Lamarque, 2001;Paoli and Schatzman, 2002), and are now summarized in reference books (Acary and Brogliato, 2008;Studer, 2009). Nonsmooth methods have been succesfully applied in a variety of contexts ranging from granular media (Renouf et al, 2004), geomaterials (Jean, 1995), multibody dynamics (Chen et al, 2013) to realistic simulations of hair motions and living systems (Acary et al, 2014;Bertails-Descoubes et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Nonsmooth contact dynamics for the numerical simulation of collisions in musical string instruments

Issanchou

Acary

Pérignon

et al. 2018

The Journal of the Acoustical Society of America

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Collisions in musical string instruments play a fundamental role in explaining the sound production in various instruments such as sitars, tanpuras and electric basses. Contacts occuring during the vibration provide a nonlinear effect which shapes a specific tone due to energy transfers and enriches the hearing experience. As such, they must be carefully simulated for the purpose of physically-based sound synthesis. Most of the numerical methods presented in the literature rely on a compliant modeling of the contact force between the string and the obstacle. In this contribution, numerical methods from nonsmooth contact dynamics are used to integrate the problem in time. A Moreau-Jean time-stepping scheme is combined with an exact scheme for phases with no contact, thus controlling the numerical dispersion. Results for a two-point bridge mimicking a tanpura and an electric bass are presented, showing the ability of the method to deal efficiently with such problems while invoking, as compared to a compliant approach, less modelling parameters and a reduced computational burden.

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Comparison of several numerical methods for mechanical systems with impacts

Cited by 26 publications

References 35 publications

Inner mass impact damper for attenuating structure vibration

Inner mass impact damper for attenuating structure vibration

Discrete Lagrangian mechanics for nonseparable nonsmooth systems

Nonsmooth contact dynamics for the numerical simulation of collisions in musical string instruments

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