Classification principles of types of mechanical systems with impacts - Fundamental assumptions and rules

Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, Poland
European Journal of Mechanics - A/Solids (Impact Factor: 1.68). 05/2004; 23(3):517-537. DOI: 10.1016/j.euromechsol.2004.02.005


The way in which subsequent types of mechanical systems with impacts with n degrees of freedom arise and their classification are shown. The presentation of classification principles is a new compilation, according to the knowledge of the authors. The paper answers the question: how many types of systems with impacts exist in general and what these types are, and it leads to numerous conclusions, as well as shows directions of future investigations. Systems with one and two degrees of freedom are considered in detail. The models of systems under consideration are rigid bodies connected by means of, for instance, springs, which can perform a motion along a straight line without a possibility of rotations. For such systems, a complete spring–impact classification has been presented. A simple way of the notation of mechanical systems with impacts, consistent with the principles of the classification developed, has been proposed. The presented classification principles of types of mechanical systems with impacts are of fundamental importance in their designing processes.

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Available from: Tomasz Kapitaniak
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    • "Phase II is an elimination phase (cf. [9]) and it consists in elimination of redundant equivalent spring-impact combinations that correspond to one physical systems (subphase I) and to eliminate combinations that are faulty due to their disconnectedness (subphase II). "
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    ABSTRACT: A structural classification method of vibro-impact systems with an arbitrary finite number of degrees of freedom based on the principles given by Blazejczyk-Okolewska et al. [Blazejczyk- Okolewska B., Czolczynski K., Kapitaniak T., Classification principles of types of mechanical systems with impacts - fundamental assumptions and rules, European Journal of Mechanics A/Solids, 2004, 23, pp. 517-537] has been proposed. We provide a characterization of equivalent mechanical systems with impacts expressed in terms of a new matrix representation, introduced to formulate the notation of the relations occurring in the system. The developed identification and elimination procedures of equivalent systems and an identification procedure of connected systems enable determination of a set of all structural patterns of vibro-impact systems with an arbitrary finite number of degrees of freedom.
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    • "The spring k 1 has been introduced so that in the mathematical model of the system under analysis there are three coefficients of stiffness, that is to say, their number is equal to the number of different terms in the symmetrical stiffness matrix of the 2-DOF mechanical system. Let us notice that the spring system, which will thus arise, will be the basic spring 2-DOF system, according to the principles of classification of mechanical systems with impacts described in [4]. It is worth mentioning that thanks to it, the system under analysis can be used, for instance, to investigate the dynamical behavior of the system consisting of a massless cantilever beam with two concentrated masses. "
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    • "Vibro-impact oscillators have moving parts colliding with either moving or stationary components, and are often found in engineering applications, as vibration hammers, driving machinery, milling, impact print hammers, and shock absorbers [1] [2]. The practical interest in the study of vibro-impact oscillators lies in both their desirable and undesirable effects. "
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    ABSTRACT: The dynamics of vibro-impact systems of engineering interest is numerically studied by means of a prototype consisting of an oscillating cart containing a ball undergoing inelastic collisions with its walls. We have described a multistable regime, for which different attractors coexist with a complicated basin boundary structure in the phase space. We investigated the effect of adding a certain amount of parametric noise in this model, focusing on the basin hopping, i.e., the intermittent switching between basins of different attractors.
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