Hindawi Publishing Corporation Journal of Nonlinear Dynamics Volume 2013, Article ID 485676, 12 pages http://dx.doi.org/10.1155/2013/485676 Research Article Comparison of Two Impact Simulation Methods Used for Nonlinear Vibroimpact Systems with Rigid and Soft Impacts V. A. Bazhenov, O. S. Pogorelova, and T. G. Postnikova Kyiv National University of Construction and Architecture, 31 Povitrofotskiy Avenue, Kyiv 03680, Ukraine Correspondence should be addressed to T. G. Postnikova; posttan@ukr.net Received 26 March 2013; Revised 16 July 2013; Accepted 18 July 2013 Academic Editor: Giovanni P. Galdi Copyright © 2013 V. A. Bazhenov et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper compares the use of two impact simulation methods for two-degree-of-freedom nonlinear vibroimpact systems with rigid and sof impacts. Tese methods are (I) impact simulation by boundary conditions with the use of Newton’s restitution coefcient based on stereomechanic shock theory and (II) impact simulation by contact interaction force based on quasistatic Hertz’s contact theory. It is shown that both methods are applied and give the coinciding results for system with elastic rigid impact under periodic external loading. Loading curves built by parameter continuation method are confrming this result. Impact simulation by the second method is also fulflled for vibroimpact system with rigid impact under random external loading. For vibroimpact system with sof impact, the simulation of impact by the second method gives a better result. Te application of linear elastic force as contact one is possible too but the use of Hertz’s contact force is more preferable. Te authors consider that the impact simulation by Hertz contact interaction force gives good results for nonlinear vibroimpact systems with impacts of any kind if all limitations with Hertz’s law used are observed. 1. Introduction Impact and vibroimpact devices are widely used in engi- neering. Teir use is described convincingly and in detail in [1]. Terefore vibroimpact processes dynamics in mechanical systems is the investigation subject of special interest that predetermines study of motion and contact interaction forces between bodies in vibroimpact systems. Such investigations are developed extensively during the last 50 years. Many monographs and papers were devoted to this topic, for example, well-known monographs [2–4]. But one can face the big difculties while solving some real and several theoretical tasks. And impact processes investigations are continued at the present too. Among the contemporary publications we want to underline such encyclopedic works as Ivanov’s [5], Ibrahim’s [6], and Stronge’s [7] monographs. A big attention is paid to stability studying in systems with impacts, periodic motions bifurcations, grazing bifurcations, singularities at vibroimpact dynamics, and other specifc problems [2, 8–12]. Let us note by a way that Ibrahim’s research monograph [6] is followed by the list of over 1100 references! From our point of view the question about impact simu- lation way, that is, the impact rule, is not of little importance in the time of the vibroimpact processes dynamics investi- gations. Ivanov in [5] writes; “Te choice of this or other impact model for exact problem solution is connected with compromise between simplicity and realistic approach. How- ever, one can achieve it rarely at practice.” Ivanov calls three model groups the most known for collinear bodies’ impact, which is examined in this paper. Firstly it is stereomechanical shock theory which considers that the period of contact is vanishingly small, so the impact is instantaneous. Tis theory uses the boundary conditions about discontinuous change in bodies’ velocities at impact and considers that the bodies are absolutelt hard and don’t have any deformation in collision. To write the impact rule one can take Newton’s coefcient of restitution which is considered to be constant and is determined by materials of the colliding bodies. It does not depend on velocity of bodies’ rapprochement or on any other circumstances. Now the development of this theory is connected with making the restitution coefcient more precise while it is not considered to be constant. Te