STATIONARY VIBRATIONS OF A SYSTEM WITH AN IMPACT ABSORBER SUBJECTED TO PERIODIC IMPULSES OF FINITE DURATION

Vestnik MGSU 4/2012
  • Dukart Adam Vilebal'dovich - Moscow State University of Civil Engineering (MSUCE) Professor, Doctor of Technical Sciences, Department of Structural Mechanics, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Thanh Binh Pham - Moscow State University of Civil Engineering (MSUCE) graduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 44 - 50

Impulsive loadings, or repetitive brief impacts, produced by machines and mechanisms of the shock action, are widely spread in the engineering practice. In many cases, trustworthy results of their dynamic analyses can be obtained by taking account of the shape and duration of their impulses.
In the paper, the periodic mode of the system motion and the parameters of the impact absorber applicable to one-sided periodic impulses of rectangular form are examined. The structure to be protected and the absorber are simulated as a system of a single collision of masses. The impacts are accepted to be instantaneous and taken into account by means of the coefficient of restitution. The damping properties of the protected structure and the absorber are considered on the basis of the viscid friction hypothesis; therefore, the damping properties of the whole system are disproportionate.
The relations identified in the course of the research are used to find the impulse frequency characteristics (IFC) of the protected structure to identify the absorber parameters. The affect of duration of external impulses produced onto the IFC, characterized by the drastic increase in the amplitudes as compared to that in the case of a single impulse of the same magnitude, is the subject of research. It is proven that the maximal ordinates of IFC decrease slightly against the increase in the duration of external impulses; therefore, the efficiency of the impact absorber changes insignificantly, and it is equivalent to that of a dynamic absorber. It is noteworthy that if the duration of external impulses is under 10 % of the duration of the period, they may be replaced by instantaneous impulses.

DOI: 10.22227/1997-0935.2012.4.44 - 50

References
  1. Dukart A.V. Zadachi teorii udarnykh gasiteley kolebaniy [Objectives of the Theory of the Impact Vibration Damper]. Moscow, ASV Publ., 2006.
  2. Korenev B.G., Rabinovich I.M., editors. Dinamicheskiy raschet zdaniy i sooruzheniy: spravochnik proektirovshchika [Dynamic Analysis of Buildings and Structures: Designer’s Reference Book]. Moscow, Stroyizdat Publ., 1981.
  3. Sorokin E.S. Osnovnye predposylki rascheta sooruzheniy na impul'sivnye nagruzki [Main Preconditions for Calculation of Structures Exposed to Impulsive Loads]. Voprosy prikladnoy mekhaniki [Problems of Applied Mechanics]. Moscow, Stroyizdat Publ., 1968, no. 260, pp. 5—37.
  4. Goldsmith V. Udar. Teoriya i fizicheskie svoystva soudaryaemykh tel [Impact. Theory and Physical Properties of Colliding Bodies]. Moscow, Stroyizdat Publ., 1965.
  5. Dukart A.V. K opredeleniyu ustanovivshikhsya kolebaniy sistemy s dvumya stepenyami svobody pri deystvii periodicheskikh impul'sov konechnoy prodolzhitel'nosti [About the Identification of Stationary Vibrations of a System That Has Two Levels of Freedom Exposed to Periodic Impulses of Finite Duration]. Izvestiya vuzov. Stroitel'stvo. [News of Higher Educational Institutions. Construction]. 2012, no. 1, pp. 3—13.

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Transient vibrations of a cantilever bar with an attachedabsorber in case of pre-set initial conditions

Vestnik MGSU 3/2013
  • Dukart Adam Vilebal’dovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Pham Viet Ngoc - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Pham Thanh Binh - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 53-60

The authors consider decaying flexural vibrations of a cantilever bar having a permanent cross section. The mass is concentrated at the free end, and the impact absorber is attached to the mass. Initial conditions are pre-set by the authors. Properties of the bar and the damper are considered in pursuance of the Е.S. Sorokin theory of frequency independent friction whereby it is accepted that the initial system demonstrates disproportionate friction.The effect of impacts is assessed using the restitution coefficient. It is assumed that vibrations of the system are described by linear differential equalizations. The Fourier method of division of variables in combination with the method of initial parameters is employed, and motion of the mass of the bar and absorber is presented in an explicit form.The solution is used to study the system behaviour exposed to the instantaneous single impulse applied to the concentrated mass at the end of the bar. The influence of parameters of dynamic and impact absorbers onto transient vibrations of the system is studied. In addition, the impact of higher modes of vibrations on overall results is estimated.

DOI: 10.22227/1997-0935.2013.3.53-60

References
  1. Korenev B.G., Reznikov L.M. Dinamicheskie gasiteli kolebaniy: teoriya i tekhnicheskie prilozheniya [Dynamic Dampers of Vibrations: Theory and Engineering Applications]. Moscow, Nauka Publ., 1988, 304 p.
  2. Vul’fson M.N. K voprosu o vybore parametrov dinamicheskogo gasitelya kolebaniy. Nelineynye kolebaniya i perekhodnye protsessy v mashinakh [On Selection of Parameters of a Dynamic Absorber. Nonlinear Vibrations and Transition Processes in Machines]. Moscow, Nauka Publ., 1972, pp. 347—354.
  3. Dukart A.V., Pham Viet Ngoc, Pham Thanh Binh. K opredeleniyu svobodnykh kolebaniy dvukhmassovoy sistemy s dempfirovaniem [On Identification of Free Oscillations of the Damped Dual-mass System]. Izvestiya vuzov. Stroitel’stvo [News of Institutions of Higher Education. Construction.] 2011, no. 5, pp. 98—106.
  4. Dukart A.V., Pham Thanh Binh. O perekhodnykh rezhimakh kolebaniy odnomassovoy sistemy s udarnym gasitelem pri zadannykh nachal’nykh usloviyakh [On Transitory Vibration Modes of a Single-mass System Exposed to the Impact Damper in Case of Pre-set Initial Conditions]. Izvestiya vuzov. Stroitel’stvo [News of Institutions of Higher Education. Construction.] 2011, no. 6, pp. 16—22.
  5. Varat S.N., Sankar S. Single Unit Impact Damper in Free and Forced Vibration. Journal of Sound and Vibration. 1985, vol. 99, no. 1, pp. 85—94.
  6. Dukart A.V. Zadachi teorii udarnykh gasiteley kolebaniy [Objectives of the Theory of Impact Vibration Dampers]. Moscow, ASV Publ., 2006.
  7. Goldsmit V. Udar. Teoriya i fizicheskie svoystva soudaryaemykh tel [Impact. Theory and Physical Properties of Colliding Bodies]. Moscow, Stroyizdat Publ., 1965.

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