Restitution modeling in vibration-dominated impacts using energy minimization under outward constraints

• Published in: International journal of mechanical sciences Vol. 166; p. 105215
• Main Authors: Bhattacharjee, Arindam, Chatterjee, Anindya
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.01.2020
• Subjects: Energy minimization; Impact; Net-impulse; Outward constraints; Vibro-impact; Impact; Vibro-impact; Energy minimization; Net-impulse; Outward constraints
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2019.105215

•Presents a new net-impulse model for restitution in vibration-dominated impacts.•Model uses a simple principle, ensures reasonable outcomes, and uses modal data.•Maximizes energy loss subject to basic inequalities and two new outward constraints.•Outward constraints enhance rebound, use three fitted parameters, and match data.•Model is demonstrated against detailed simulation data from ball-beam impacts. [Display omitted] Impact models can involve either detailed simulation or approximate net-impulse prediction. Net-impulse approaches map pre-impact to post-impact states without solving differential equations. Net-impulse approaches are seldom used for predicting restitution in vibration-dominated impacts with explicit accounting of vibrations. Here we study impacts of Hertzian balls on four different Euler-Bernoulli beams, with uniform and nonuniform cross sections as well as different boundary conditions. For each beam, initial detailed simulations using modal coordinates are used to compute restitution values for different ball masses and contact locations. Subsequently, a simple method is proposed for approximately predicting the restitution level, given colliding mass and vibration mode information. The key idea is to minimize post impact kinetic energy subject to various linear inequality constraints. These constraints include both fundamental restrictions as well as new outward or rebound-enhancing constraints that constitute the main novelty of the approach. The new approach, referred to as Energy Minimization under Outward Constraints (EMOC), requires solution of a quadratic optimization problem, yields a unique solution using readily available routines, and has three fitted parameters. These parameters, in our examples, are constant for all ball masses and contact locations for a given beam. Physical impossibilities like interpenetration or energy increases are never predicted for any parameter values. Upon parameter fitting, the match between full numerical solution and EMOC is good on average, with key qualitative trends captured correctly. No comparable net-impulse model exists in the vibroimpact literature.