Abstract
A new technique to simulate nonsmooth motions occurring in vibro-impacting continuous systems is proposed. Sticking motions that are encountered during vibro-impact simulation are imposed exactly using a Lagrange multiplier, which represents the normal reaction force between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The developed theory is demonstrated by numerically simulating the forced response of a pinned-pinned beam impacting a point-like rigid obstacle.
Highlights
The dynamics of continuous systems like beams, strings, and rods subjected to impacts caused by motion-limiting constraints have been studied extensively
We propose a new method to simulate the beam motion during the sticking phase which does not require the reevaluation of mode shapes with a pin at the location of impact, enabling the efficient handling of sticking motions within the CoR method
The pre-impact velocity continually drops and approaches zero.To switch to the sticking motion phase the time between two successive impacts is monitored and when this time falls below a certain threshold, the beam is assumed to stick with the obstacle
Summary
The dynamics of continuous systems like beams, strings, and rods subjected to impacts caused by motion-limiting constraints have been studied extensively. We propose a new method to simulate the beam motion during the sticking phase which does not require the reevaluation of mode shapes with a pin at the location of impact, enabling the efficient handling of sticking motions within the CoR method. This is done by deriving closed form expressions for the reaction force at the pin such that the gap constraint is exactly enforced. A suitable numerical example will be shown to demonstrate this method on a vibroimpacting supported beam
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