Klasyfikacja układów mechanicznych ze zderzeniami

Błażejczyk-Okolewska, B.

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Tytuł artykułu

Klasyfikacja układów mechanicznych ze zderzeniami

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Błażejczyk-Okolewska B.

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Warianty tytułu

Classification of mechanical systems with impacts

Języki publikacji

Abstrakty

Znaczny wzrost zainteresowania badaniem coraz bardziej złożonych układów mechanicznych ze zderzeniami, a także mnogość i różnorodność takich układów sprawiają, że zachodzi potrzeba ich sklasyfikowania. Analiza porównawcza modeli fizycznych układów wibrouderzeniowych doprowadziła autora do zdefiniowania pojęcia typu układu oraz sformułowania zasad klasyfikacji układów o dowolnej liczbie stopni swobody. Kryteria klasyfikacji zostały zaproponowane w oparciu o aspekty dynamiczne poruszane w literaturze przedmiotu i uwzględniają występowanie w układach dowolnego połączenia oraz dowolnego rodzaju wymuszenia zewnętrznego. Typem układu mechanicznego ze zderzeniami jest pewna seria układów o określonej budowie elementów składowych (konfiguracja zderzaków i połączeń) oraz określonych cechach charakterystycznych (konfiguracja wymuszeń zewnętrznych). Wszystkie typy układów mechanicznych stanowią zbiór, w którym rodzaj połączeń (sprężyna lub tłumik) i ich charakter (liniowość lub nieliniowość), rodzaj wymuszeń zewnętrznych (dynamiczny lub kinematyczny) oraz sposób modelowania zjawiska zderzeń nie są parametrami różnicującymi. Opracowana metoda klasyfikacji została zastosowana do sklasyfikowania układów ze zderzeniami o jednym i o dwóch stopniach swobody. Wyznaczono wszystkie typy takich układów. Podzielono je na rodziny kierując się następującymi kryteriami: liczbą stopni swobody, liczbą przyłożonych wymuszeń zewnętrznych, liczbą zderzaków w strefie spójności zderzakowej i liczbą dowolnych połączeń. W ramach każdej rodziny wyróżniono typy układów o określonej liczbie i konfiguracji zderzaków zewnętrznych oraz określonych konfiguracjach dowolnych połączeń i wymuszeń zewnętrznych. Kolejnym typom nadano numery, które nazwano numerami typów. Zmontowanie układu oraz dochodzenie w nim do określonych zderzeń, jest uzależnione od wymiarów poszczególnych podukładów. W pracy podano warunki geometryczne montażu oraz warunki geometryczne zderzeń zewnętrznych i wewnętrznych dla układów o jednym i o dwóch stopniach swobody. Stanowią one pewnego rodzaju kryterium pozwalające na określenie typu konkretnego układu. Proponowana przez autora klasyfikacja układów mechanicznych ze zderzeniami według cech charakterystycznych ich struktury, wydaje się być klasyfikacją naturalną. Odzwierciedla ona pokrewieństwo budowy układów, mówi o ich drodze ewolucyjnej i przedstawia ich genezę. Pozwala uporządkować wiedzę o układach z uderzeniami oraz stanowi podstawę do zrozumienia źródeł ich różnorodności. Dając pełny zestaw przedmiotów analizy, udziela wskazówek co do rozwoju nowych myśli i kierunków w projektowaniu urządzeń technicznych.

A significant increase of interest in investigations of more and more complex mechanical systems with impacts as well as a large number of such systems and their variability cause that a need to classify them arises. The comparative analysis of physical models of vibro-impact systems has led the author to a definition of a type of the mechanical system with impacts and a formulation of classification principles of all systems with an arbitrary number of degrees of freedom. The classification criteria have been proposed on the basis of all dynamic aspects considered in the literature devoted to the subject. They account for an occurrence of an arbitrary connection and an arbitrary kind of external excitation in systems. By a type of the mechanical system with impacts is understood a certain series of systems characterized by a specified structure of component elements (a definite configuration of fenders and connections) and specified characteristics (an application of the definite configuration of external excitations). All types of mechanical systems constitute a set in which a kind of the connection (a spring or a damper) and its character (linearity or nonlinearity), a kind of external excitations (dynamic or kinematic) and a way the impact phenomenon is modelled are not differentiating parameters. The developed method has been applied to classify systems with impacts with one and two degrees of freedom. All types of such systems have been determined and then divided into groups using the following criteria: a number of degrees of freedom, a number of external excitations applied, a number of fenders in the zone of fender aptness and a number of possible connections. Within each group, types of systems with a definite number and a configuration of outer fenders and definite configurations of arbitrary connections and external excitations have been recognized. Individual types have been referred to by numbers that have been called numbers of these types. The fact that the dimensions of separate subsystems are taken into account causes that they have to fulfil certain geometrical conditions that allow for the system assembly and to satisfy certain geometrical conditions that make outer and inner impacts possible in the system. In the present dissertation, the conditions for a system with one degree of freedom and with two degrees of freedom have been given. They yield a certain criterion that allows for identifying a type of the given system with impacts. This study provides numerous data that extend the knowledge on mechanical systems with impacts. In future, this information can be used in designing such structures. The knowledge of properties of individual types of systems and principles of their formation can be helpful in solving various technical tasks that fall beyond the scope of traditional applications.

Słowa kluczowe

uderzenia układ mechaniczny układy sprężynowo-zderzakowe

impacts mechanical system

Wydawca

Wydawnictwo Politechniki Łódzkiej

Czasopismo

Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka

Rocznik

2005

Tom

Z. 343

Strony

3--117

Opis fizyczny

Bibliogr. 98 poz.

Twórcy

autor

Błażejczyk-Okolewska B.

Katedra Dynamiki Maszyn Politechniki Łódzkiej

Bibliografia

[1] Aidanpaa J.O., Gupta R.B.: Periodic and Chaotic Behaviour of a Threshold-Limited Two-Degree-of Freedom System. Journal of Sound and Vibration, 165(2), 1993, 305-307.
[2] Araki Y., Yokomichi I. and Inoue J.: Impact Dampers with Granular Materials (4th Report). Bulletin of the Japanese Society of Mechanical Engineers, 29(258), 1986, 4334-4338.
[3] Arnold R.N.: Response of an impact vibration absorber to forced vibration. Proceedings of the Ninth International Congress of Applied Mechanics. Brussels, 1956.
[4] Awrejcewicz J. and Lamarque C-H.: Bifurcation and chaos in nonsmooth dynamical systems. World Scientific Series in Nonlinear Science, Series A. World Scientific Publishing Co. Singapore. 2003
[5] Babitskii V.l.: Existence of high frequency oscillations of large amplitudes in linear system with limiters. Mashinovedeni, No 1 (in Russian), 1966, 22-25.
[6] Babitskii V.l.: Theory of Vibroimpact Systems. Moscow: Nauka (in Russian), 1978.
[7] Babitsky V.l., Krupenin V.L.: Vibrations in strongly nonlinear systems. Moscow: Nauka (in Russian), 1985.
[8] Bajkowski J.: Modeling of shock absorbers with dry friction subjected in impact loads. Machine Dynamics Problems, 16,1996,7-19.
[9] Bapat C.N.: Periodic motions of an impact oscillator. Journal of Sound and Vibration, 209(1), 1998,43-60.
[10] Bapat C.N. and Sankar S.: Multi-unit impact damper. Journal of Sound and Vibration, 103(4), 1985, 457-469.
[11] Barkan D.D., Shekhter O.J.: 1) Theory of forced vibrations of the oscillator with the constrain. 2) Forced vibrations of the oscillator with the moving constraint. Zhurnal Tekhnicheskoi Fisiki, Vol. XXV, No. 13 (in Russian), 1955.
[12] Barkan D.D., Shekhter O.J.: 1) To the Theory of Forced Vibration of a Vibrator With Stops. 2) Forced Vibrations of a Vibrator With Moving Stop. Zhurnal Tekhnicheskoi Fisiki, Vol. XXV, No. 13 (in Russian), 1955.
[13] Bespalowa L.V.: On the theory of the vibro-impact system. Izv. AN SSSR, OTN (in Russian), 5,1957,3-14.
[14] Bishop S.R.: Impact oscillators. Phil. Trans. Royal Society London, A 347, 1994, 347-351.
[15] Blazejczyk-Okolewska B.: Analysis of an impact damper of vibrations. Chaos, Solitons & Fractals, 12, 2001,1983-1988.
[16] Blazejczyk-Okolewska B., Czolczynski K.: Some aspects of the dynamical behaviour of the impact force generator. Chaos, Solitons & Fractals, 9, 1998,1307-1320.
[17] Blazejczyk-Okolewska B., Kapitaniak T.: Dynamics of Impact Oscillator with Dry Friction. Chaos, Solitons & Fractals, 7(1), 1996, 1-5.
[18] Blazejczyk-Okolewska B. and Kapitaniak T.: Co-existing attractors of impact oscillator. Chaos, Solitons & Fractals, 9(8), 1998, 1439-1443.
[19] Błażejczyk B„ Kapitaniak T., Wojewoda J. and Barron R.: Experimental observation of intermittent chaos in a mechanical system with impacts. Journal of Sound Vibration, 178, 1994, 272-275.
[20] Blazejczyk-Okolewska B., Czolczynski K.: Dynamics of the linear oscillator with impacts. Mechanics and Mechanical Engineering, 3(1), 1999, 5-14.
[21] 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, 23, 2004, 517-537.
[22] Blazejczyk-Okolewska, B., Czolczynski, K., Kapitaniak, T., Wojewoda, J.: Chaotic Mechanics in Systems with Impacts and Friction. World Scientific Series in Nonlinear Science, Series A. World Scientific Publishing Co. Singapore 1999.
[23] Blazejczyk-Okolewska B., Brindley J., Czolczynski K. and Kapitaniak T.: Antiphase synchronization of chaos by noncontinuous coupling: two impacting oscillators. Chaos, Solitons & Fractals, 12, 2001,1823-1826.
[24] Brach R.M.: Mechanical Impact Dynamics. Rigid Body Collisions. John Wiley and Sons, Inc., 1991.
[25] Brogliato B.: Nonsmooth Mechanics. Springer, 1999.
[26] Cempel C: Okresowe drgania z uderzeniami w dyskretnych układach mechanicznych. Politechnika Poznańska, Poznań, Rozprawy No 44, 1970.
[27] Cempel C: The multi-unit impact damper: equivalent continuous force approach. Journal of Sound and Vibration, 34(2), 1974, 199-209.
[28] Cempel C: Receptance model of the multi-unit impact neutralizer - MUVIN. Journal of Sound and Vibration, 40(2), 1975, 249-266.
[29] Cempel C. and Lotz G.: Efficiency of vibrational energy dissipation by moving shot. Journal of Strucural Engineering, 119(9), 1993, 2643-4652.
[30] Cempel C. and Natke H.G.: Shot Vibration damper - an equivalent energy approach. Abhandlungen der Braunschw. Wissenschaftl, Gersellschaft, Band XLI, 1989,87-100.
[31] Chen G.: Controlling Chaos and Bifurcations in Engineering Systems. CRC Press LLC, 2000.
[32] Chin W., Ott E., Nüsse H.E., Grebogi C: Grazing bifurcation in impact oscillators. Physical Review E, 50(6), 1994, 4427-4444.
[33] Chin W., Ott E., Nusse H.E., Grebogi C: Universal behavior of impact oscillators near grazing incidence. Physics Letters A, 201, 1995, 279 -297.
[34] Czolczynski K.: On the existence of a stable periodic motion of two impacting oscillators. Chaos, Solitons & Fractals, 15, 2003,371-379.
[35] Czolczynski K. and Kapitaniak T.: Influence of the mass and stiffness ratio on a periodic motion of two impacting oscillators. Chaos, Solitons & Fractals, 17, 2003, 1-10.
[36] Dąbrowski A.: Dynamika wibracyjnego tłumika drgań z ogranicznikami amplitudy ruchu. Praca Doktorska, Politechnika Łódzka, Łódź, 2002.
[37] Deo N.: Teoria grafów i jej zastosowania w technice i informatyce. PWN, Warszawa, 1980.
[38] Di Bernardo M., Feigin M. I., Hogan S. J. and Homer M. E.: Local Analysis of C-Bifurcation in n - Dimensional Piecewise-Smooth Dynamical Systems. Chaos, Solitons & Fractals, 10, 1999,1881-1908.
[39] Feigin M. I.: Behaviour of dynamical systems near the existence boundaries of periodic motions. PMM (in Russian), 41(4), 1977, 628-636.
[40] Foale S., Bishop S.R.: Dynamical Complexities of Forced Impacting Systems. Phil. Trans, of the Royal Soc. of London A, 338, 1992, 547-556.
[41] Fu C.C., Paul B.: Dynamic stability of a vibrating hammer. Journal of Engineering for Industry, Trans. ASME B, 91, 1969,1175-1179.
[42] Giergiel J., Uhl T.: Identyfikacja układów mechanicznych. PWN, W-wa, 1990.
[43] Goldsmith W.: Impact. Arnold LTD, London, 1960.
[44] Goyda H., The CA.: A Study of the Impact Dynamics of Loosely Supported Heat Exchanger Tubs. ASME J. Pressure Tech., III, 1989, 394-401.
[45] Grubin, C: On the Theory of the Acceleration Damper. Journal of Applied Mechanics, 23(3), 1956.
[46] Gryboś R.: Teoria uderzenia w dyskretnych układach mechanicznych. PWN, W-wa, 1969.
[47] Guckenheimer J. and Holmes, P.J.: Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. Springer-Verlag, New York, 1983.
[48] Heiman M.S., Bajaj A.K., Shennan P.J.: Periodic Motions and Bifurcations in Dynamics of an Inclined impact Pair. Journal of Sound and Vibrations, 124(1), 1988,55-78.
[49] Hinrichs N., Oestreich M., Popp K.: Dynamics of oscillators with impact and friction. Chaos, Solitons & Fractals, 8(4), 1997, 535-558.
[50] Horak Z.: General static theory of impact of rough bodies. Internat. Congress of Appl. Mechanics, Brussels, Book of Abstracts section II, p.III/139a-c, 1956.
[51] Irie T., Yamada G., Matsuzaki H.: On the dynamic response of a vibro-impact system to random force. Bull, of the Faculty of Engineering, Hokkaido University, 72, 1974, 13-24.
[52] Isomaki H., Boehm J., Raty R.: Devil's attractors and chaos of a driven impact oscillator. Physics Letters A, 107, 1985, 343-346.
[53] Ivanov A.P.: Stabilization of an impact oscillator near grazing incidence owing to resonance. Journal of Sound and Vibration, 162, 1993, 562-565.
[54] Ivanov A.P.: Impact oscillations: linear theory of stability and bifurcations. Journal of Sound and Vibration, 178,1994, 361-378.
[55] Kaharaman A., Singh R.: Nonlinear Dynamics of a Spur Gear Pair. Journal of Sound and Vibration, 142, 1990, 49-75.
[56] Kapitaniak T.: Chaotic oscillations in mechanical systems, Nonlinear Science - theory and applications. Manchester and New York, 1991.
[57] Ketema Y.: An oscillator with cubic and piecewise-linear springs. International J. of Bifurcation and Chaos, 1(2), 1991, 349-356.
[58] Kobrinskii A.E.: Mechanisms with elastic coupling. Moscow, Nauka (in Russian), 1964, see also the translation to English: Dynamics of Mechanisms with Elastic Connections and Impact Systems. Iliffe Book LTD, London, 1969,1-363.
[59] Kobrinskii A.E., Kobrinskii A.: Vibroimpact System. Moscow: Nauka Press (in Russian), 1973.
[60] Koizumi, K.: Analysis of vibration with collision and applications to leaf beating machine. Doctor Thesis, University of Tokyo, Precision Mechanical Engineering (in Japanese), 1980.
[61] Lieber P., Jensen D.: An acceleration damper: development, design and some application. Trans. oftheASME, 67, 1945, 523-530.
[62] Lin S.Q., Bapat C.N.: Estimation of clearances and impact forces using vibroimpact responce: random excitation. Journal of Sound and Vibration, 163, 1993,407-421.
[63] Luo G.W., Xie J.H.: Hopf bifurcations and chaos of a two-degree-of-freedom vibro-impact system in two strong resonance cases. International Journal of Non-Linear Mechanics, 37,2002, 19-34.
[64] Masri S.F.: Analytical and experimental studies of multi-unit impact dampers. The Journal of the Acoustical Society of America, 45(5), 1964, 1111-1117.
[65] Masri S.F., Caughey T.K.: On the stability of the impact damper. Journal of Applied Mechanics, 33, 1966, 586-592.
[66] Masri S.F., Ibrahim A.M.: Stochastic excitation of a simple system with impact damper. Earthquake Engineering and Structural Dynamics, 1, 1973, 337-346.
[67] Moon F.C.: Chaotic Vibrations. J. Wiley & Sons, New York, 1987.
[68] Morecki A., Oderfeld J.: Teoria maszyn i mechanizmów. PWN, W-wa, 1987.
[69] Natsiavas S.: Stability and bifurcation analysis for oscillators with motion limiting constraints. Journal of Sound and Vibration, 141, 1990, 97-102.
[70] Natsiavas S.: Dynamics of multiple-degree-of-freedom oscillators with colliding components. Journal of Sound and Vibration, 165, 1993, 439-453.
[71] Nguyen D.T., Noah S.T., Kettleborough CF.: Impact behavior of an oscillator with limiting stops (part I and II). Journal of Sound and Vibration, 109, 1987, 293-325.
[72] Nigm M.M., Shabana A.A.: Effects of an impact damper on a multidegree of freedom system. Journal of Sound and Vibration, 89, 1983, 541-557.
[73] Nordmark A.B.: Non-Periodic Motion Caused by Grazing Incidence in an Impact Oscillator. Journal of Sound and Vibration, 145(2), 1991,279-297.
[74] Nordmark A.B.: Effects due to low velocity impact in mechanical oscillators. Technical Report from Royal Institute of Technology, Department of Mechanics, Sweden, 1992.
[75] Olachowski K.: Boring bar vibration attenuation by shot damper. MS Thesis, Poznan, University of Technology, Poznan, Poland, 1988.
[76] Osiński Z.: Teoria drgań. PWN, W-wa, 1978.
[77] Osiński Z.: Tłumienie drgań mechanicznych. PWN, W-wa, 1979.
[78] Paget A.: Vibration of steam-turbine buckets and damping by impact. Engineering, 19, No 111, 1937.
[79] Park W.H.: Mass-spring-damper response to repetitive impacts. Trans, of the ASME, Journal of Eng. for Industry, 1967, 587-596.
[80] Peterka F.: An investigation of the motion of impact dampers, paper I, II, III. Strojnicku CasopisXXl, c.5,1971.
[81] Peterka F.: Introduction to vibration of mechanical systems with internal impacts. Academia. Praha. 1981.
[82] Peterka F., Blazejczyk-Okolewska B.: Some Aspects of the Dynamical Behavior of the Impact Damper. Journal of Vibration and Control, przyjęty do druku.
[83] Peterka F., Ciepera S.: Chaotic motions in mechanical systems with impacts.Euromech Colloquium 308: Chaos and noise in dynamical systems, Lodz-Spala, Poland, 1993.
[84] Peterka F., Vacik J.: Transition to Chaotic Motion in Mechanical System with Impacts. Journal of Sound and Vibration, 154, 1992, 95-115.
[85] Popp K., Stelter P.: Nonlinear oscillations of structures induced by dry friction. Proc. of the IUTAM Symp. on Nonlinear Dynamics in Engineering Systems, Springer-Verlag, Berlin, Heidelberg, 1989, 233-240.
[86] Popplewell N., McLachlan K., Arnold J., Chang CS., and Bapat C.N.: Quiet and effective vibroimpact attenuation of boring bar vibration. Proc. of the 11th Congress on Acoustics, Paris, paper 54, 1983,1-4.
[87] Rand R.H., Moon F.C.: Bifurcations and Chaos in Forced Zero-Stiffness Impact Oscillator. Int. J. Non Linear Mechanics, 25(4), 1990, 417-432.
[88] Ratajczak R.: The multidirectional shot damper. Master Thesis, Applied Mechanics Institute, Technical University of Poznan, Poznan, Poland, 1987.
[89] Sadek M.M.: The behaviour of the impact damper. Proc. Inst. Mech Engrs, 180, 1965-1966,895-906.
[90] Senator M.: Existence and stability of periodic motions of a harmonically forced impacting systems. Journal of Acoustical Society of Amenez, 47, 1970, 1390-1397.
[91] Shaw S.W., Holmes P.J.: A Periodically Forced Piecewise Linear Oscillator. Journal of Sound and Vibration, 90, (1), 1983, 129-155.
[92] Thompson J.H.T., Bishop S.R.: Nonlinearity and Chaos in Engineering Dynamics. John Wiley and Sons, 1994.
[93] Thompson J.M.T.: Complex dynamics of compliant off-shore structures. In: Chaotic oscillators: theory and application edited by T. Kapitaniak. World Scientific: Singapore, New Jersey, London, Hong Kong, 1992, 331-351.
[94] Thompson J.M.T., Ghaffari R.: Chaos after period-doubling bifurcation in the resonance of an impact oscillator. Physics Letters A, 91, 1982, 5-8.
[95] Thompson J.M.T., Ghaffari R.: Chaotic dynamics of an impact oscillator. Physics Letters A, n, 1983, 1741-1743.
[96] Thompson J.M.T., Stewart H.B.: Nonlinear Dynamics and Chaos. John Wiley and Sons, 1986.
[97] Tung P.C., Shaw S.W.: The Dynamics of an Impact Print Hammer. ASME J. Vibration Stress Reliability in Design, 110,1998, 193-199.
[98] Wiercigroch M.: Bifurcation analysis of harmonically excited linear oscillator with clearance. Chaos, Solitons and Fractals, 4, 1994, 297-303.

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