MS08.1: Non-Smooth Dynamics

We present a novel return map approach for studying the global dynamics of a vibro-impact (VI) pair, that is, a ball moving in a harmonically forced capsule. Computationally efficient short-time realizations divide the state space according to different dynamics. A small collection of reduced piece-wise polynomial approximations yields a composite map capturing transients and reproducing bifurcation sequences of the full system. Valuable for cobweb analysis, this framework inspires auxiliary maps based on the extreme bounds of the maps, yielding global dynamics of energetically favorable states. We apply this framework to understand stochastically enhanced bi-stability for parameter regions exhibiting grazing and noise-sensitive biases. Results are relevant for recent designs of VI-based energy harvesters and nonlinear energy transfer.

This work studies a computational approach aimed at establishing equivalent dynamical responses within oscillatory impacting systems subject to soft and rigid constraints. The proposed method incorporates an adaptive differential evolution algorithm with the Metropolis criterion to determine the stiffness and damping parameters of the soft constraint for a prescribed coefficient of restitution governing the rigid constraint. This algorithm aims to achieve equal energy dissipation between the two constraints. Upon examining the dynamical responses of the two impact cases, they exhibit nearly identical outcomes in the two-parameter bifurcation diagrams when subjected to a large restitution coefficient. However, discrepancies arise when the restitution coefficient is low. Detailed numerical tests, conducted using the proposed method, demonstrate enhanced effectiveness compared to previous techniques, such as the prediction formulae outlined by Okolewski and Blazejczyk-Okolewska (Chaos, 31:083110, 2021).

Contact simulation is an important yet challenging topic for mechanical systems, especially when the system includes flexible bodies. Common collision detection methods have a trade-off between accuracy and efficiency, which influences the performance of the dynamic simulation. In this work, contact simulation using a curve-based collision detection method is proposed for flexible bodies represented in the framework of the floating frame of reference formulation. Case studies of contact between flexible beams have been implemented to demonstrate the accuracy and efficiency of such a method.

This paper presents a novel formulation for multibody systems with unilateral interactions. We address the forward dynamics simulation problem in which the dynamics formulation is solved under given loads, and as a result, the motion is determined. This simulation problem involves two main parts: the solution of the dynamics problem, momentum/velocity update, and the solution of a kinematics problem, position update. For the dynamics problem, rigid bodies are modelled using equimomental systems of point masses. After determining the velocities of the point masses with such a model, the kinematics problem is solved using the rigid body representation. With the proposed approach, the accuracy of smooth and nonsmooth problems may be improved using first-order integration methods.