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.
    Mathematical Problems in Engineering 12/2012; 2013. DOI:10.1155/2013/757980 · 0.76 Impact Factor
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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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    ABSTRACT: Impacts in mechanical systems are an object of interest for many scientists in the world. In this paper, we present detailed investigations of the dynamical behavior of the system consisting of a massless cantilever beam with two concentrated masses. The maximum displacement of one of the masses is limited to the threshold value by a rigid stop, which gives rise to non-linearity in the system. Impacts between the mass and the basis are described by a coefficient of restitution. The conducted calculations show a good agreement of the results obtained with two qualitatively different methods of behavior analysis of the system under consideration, namely: the Peterka’s method and the method of numerical integration of motion equations. It has been observed that stable solutions describing the motion with impacts of a two-degree-of freedom mechanical system exist in significantly large regions of the parameters that describe this system. The location and size of periodic motion regions depend strongly on mutual relations between the excitation force frequency and the system eigenvalues. In order to obtain stable and periodic motion with impacts, the system parameters should be selected in such a way as to make the excitation force frequency an even multiple of the fundamental eigenvalue and to make the higher eigenvalue an even multiple of the excitation force frequency. These two conditions can be applied in designing mechanical systems with impacts. This information is even of more significance since it has turned out that the system exhibits some adaptability, owing to which stable solutions exist even if the above-mentioned conditions are satisfied only approximately.
    Chaos Solitons & Fractals 05/2009; 40(4). DOI:10.1016/j.chaos.2007.09.097 · 1.45 Impact Factor
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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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