Modal Analysis of Mechanical Systems With Impact Non-Linearities: Limitations to a Modal Superposition

Lamarque, Claude‐Henri; Janin, O.

doi:10.1006/jsvi.1999.2932

Cited by 24 publications

(9 citation statements)

References 59 publications

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“…However, the friction force between M and m is neglected. The motion of the system can be treated as a piecewise linear process (Lamarque and Janin, 2000).…”

Section: Structure Modelmentioning

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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“…However, the friction force between M and m is neglected. The motion of the system can be treated as a piecewise linear process (Lamarque and Janin, 2000).…”

Section: Structure Modelmentioning

confidence: 99%

Inner mass impact damper for attenuating structure vibration

Jian

2006

International Journal of Solids and Structures

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“…[11,12] among many others). Nevertheless, very few works tackle such systems with no external periodic forcing, with the aim of identifying nonlinear modes of vibration [13,14,15,16,17]. The latter are commonly defined as continuous families-continuity with respect to the energy-of periodic orbits in the phase space.…”

Section: Introductionmentioning

confidence: 99%

Nonsmooth Modal Analysis: Investigation of a 2-DOF Spring-Mass System Subject to an Elastic Impact Law

Thorin

Legrand

Junca

2015

Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

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The well-known concept of normal mode for linear systems has been extended to the framework of nonlinear dynamics over the course of the 20th century, initially by Lyapunov, and later by Rosenberg and a growing community of researchers in modal and vibration analysis. This effort has mainly targeted nonlinear smooth systems — the velocity is continuous and differentiable in time — even though systems presenting nonsmooth occurrences have been increasingly studied in the last decades to face the growing industrial need of unilateral contact and friction simulations. Yet, these systems have nearly never been explored from the standpoint of modal analysis. This contribution addresses the notion of modal analysis of nonsmooth systems. Developments are illustrated on a seemingly simple 2-dof autonomous system, subject to unilateral constraints reflected by a perfectly elastic impact law. Even though friction is ignored, its dynamics appears to be extremely rich. Periodic solutions are sought for given numbers of impacts per period and nonsmooth modes are illustrated for one and two impacts per period in the form of two-dimensional manifolds in the phase space. Also, an unexpected bridge between these modes in the frequency-energy plots is observed.

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“…Most occurrences in the literature of the terminology multiple impacts are related to impact oscillators with several unilateral constraints (see some of the references above or [24,26]); here, multiple impacts per period refers to the same contact condition being activated several times during one period. Periodic motions with multiple impacts per period have sometimes been mentioned for forced systems [17,22,25,33] but never systematically explored. Recently, a spring-mass system subject to a purely elastic impact law with one impact per period has been thoroughly investigated [20].…”

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confidence: 99%