Prediction of period-1 impacts in a driven beam

Bishop, Steven R.; Thompson, M.; Foale, S.

doi:10.1098/rspa.1996.0137

Cited by 35 publications

(19 citation statements)

References 23 publications

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“…We will use the law (5) to describe the impacts between w and z. As a consequence the velocity y − just before impact will, in general, be different from the velocity y + just after impact.…”

Section: The System Studiedmentioning

confidence: 99%

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Corner bifurcations in non-smoothly forced impact oscillators

Budd

Piiroinen

2006

Physica D: Nonlinear Phenomena

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Section: The System Studiedmentioning

confidence: 99%

“…The dynamics of impacting mechanical systems has been the subject of much recent investigation, as it is known that even very simple systems can have very rich dynamics [1,2,3,4,5,11,15,16,18,22,25,30,31,32,35,36,37,39,38]. An example of such a simple system is the (so-called) single degree of freedom oscillator.…”

Section: Introductionmentioning

confidence: 99%

Corner bifurcations in non-smoothly forced impact oscillators

Budd

Piiroinen

2006

Physica D: Nonlinear Phenomena

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“…Although robust computational techniques now exist to simulate the constrained motion of rigid multibody systems (Brogliato 1996;Glocker 2001;Leine and Nijmeijer 2004;Acary 2008;Leine 2008), methods to analyze the impact behavior of continuous compliant systems remain an active area of research. Recognizing that beamlike structures are prevalent in industrial applications (Andrews et al 1996;Bishop et al 1996;Wagg and Bishop 2002;Ibrahim 2009), this paper focuses on formulating an efficient technique to compute the fast dynamics of a beam colliding with rigid obstacles.…”

Section: Introductionmentioning

confidence: 99%

Fast In-Plane Dynamics of a Beam with Unilateral Constraints

2017

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A computationally efficient technique to simulate the dynamic response of a beam colliding with rigid obstacles is described in this paper. The proposed method merges three key concepts. First, a low-order discretization scheme that maximizes the number of nodes of the discrete model (where impacts are detected) at the expense of the degree of continuity of the constructed displacement field is used. Second, the constrained problem is transformed into an unconstrained one by formulating the impact by using a Signorini complementarity law involving the impulse generated by the collision and the preimpact and postimpact velocity linked through a coefficient of restitution. Third, Moreau's midpoint time-stepping scheme developed in the context of colliding rigid bodies is used to advance the solution. The algorithm is first validated on the nonimpact problem of a cantilever Rayleigh beam subjected to an impulsive discrete load. Then the problem of a cantilever beam vibrating between two (symmetrically located) stops is analyzed. Both cases of discrete and continuous obstacles are considered, and the numerical predictions are compared with published results or those obtained with a commercial code.

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“…A coefficient of restitution (COR) rule is used to model the impact process as it provides a computationally simple model which has been shown (for single degree of freedom systems) to have close correlation with physical impact experiments [Thompson & Stewart 2002;Moon & Shaw 1983;Bishop, Thompson & Foale 1996]. We use an instantaneous coefficient of restitution rule which has been shown to be a suitable model for systems where the impact time is "short" compared with the time in between impacts [Wagg, Karpodinis & Bishop 1999].…”

Section: A Coefficient Of Restitution Rule For Multiple Constraintsmentioning

confidence: 99%

Dynamics of a Two Degree of Freedom Vibro-Impact System With Multiple Motion Limiting Constraints

Wagg

Bishop

2004

Int. J. Bifurcation Chaos

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We consider the dynamics of impact oscillators with multiple degrees of freedom subject to more than one motion limiting constraint or stop. A mathematical formulation for modelling such systems is developed using a modal approach including a modal form of the coefficient of restitution rule. The possible impact configurations for an N degree of freedom system are considered, along with definitions of the impact map for multiply constrained systems.We consider sticking motions which occur when a single mass in the system becomes stuck to an impact stop, and discuss the computational issues related to computing such solutions.Then using the example of a two degree of freedom system with two constraints we describe exact modal solutions for the free flight and sticking motions which occur in this system. Numerical examples of sticking orbits for this system are shown and we discuss identifying the region, S in phase space where these orbits exist. We use bifurcation diagrams to indicate differing regimes of vibro-impacting motion for two different cases; firstly when the stops are both equal and on the same side (i.e. the same sign) and secondly when the stops are unequal and of opposing sign. For these two different constraint configurations we observe

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Prediction of period-1 impacts in a driven beam

Cited by 35 publications

References 23 publications

Corner bifurcations in non-smoothly forced impact oscillators

Corner bifurcations in non-smoothly forced impact oscillators

Fast In-Plane Dynamics of a Beam with Unilateral Constraints

Dynamics of a Two Degree of Freedom Vibro-Impact System With Multiple Motion Limiting Constraints

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