Theoretical Analysis of Damping Properties of two-Degree-of-Freedom Linear Vibrational Systems

Abstract

Analytical solutions for complete two-degree-of-freedom (2 DOF) vibrational systems comprising primary and secondary resilient and damping elements and subjected to a harmonic base excitation are obtained for the first time and presented in terms of transmissibility of primary and secondary mass and resonance and invariant frequencies of primary mass, which is considered to be the object of isolation. Analytical expressions for optimum values of main system parameters including primary and secondary dampings, mass ratio and secondary and primary springs stiffness ratios are also newly presented. Damping properties of systems are analysed for the case of a constant optimum damping, which minimizes the primary mass transmissibility at the lowest resonance frequency, and for the case of frequency-variable optimum damping, providing the minimization over the entire range of forced frequency. The expressions for optimum primary and secondary dampings are given in the form of quadratic algebraic equations for the case of complete 2 DOF systems. The influence of the mass and spring stiffness ratios on the system response is investigated as well. The obtained results, being of a general nature and obtained for large ranges of main parameters, can be applied to different classes of vibration isolation problems, such as isolation of a large item of machinery, a light piece of instrumentation or a ground vehicle.

Keywords

two-degree-of-freedom systems vibration absorbers linear damping

Get full access to this article

View all access options for this article.

References

Ormondroyd

Hartog

J. P.

Theory of dynamic vibration absorber. Trans. ASME, 1928, 50, A9–A22.

Snowdon

J. C.

Vibration and shock in damped mechanical systems, 1968 (John Wiley, New York).

Snowdon

J. C.

Dynamic vibration absorbers that have increased effectiveness. Trans. ASME J. Engng Industry, 1974, B96, 940–945.

Nobile

M. A.

Snowdon

J. C.

Viscously damped dynamic absorbers of conventional and novel design. J. Acoust. Soc. Am., 1977, 61(5), 1198–1208.

Bapat

V. A.

Kumaraswamy

H. V.

Effect of primary system damping on the optimum design of an untuned viscous dynamic vibration absorber. J. Sound Vibr., 1979, 63(4), 469–474.

Thompson

A. G.

Auxiliary mass throw in a tuned and damped vibration absorber. J. Sound Vibr., 1980, 70(4), 481–486.

Thompson

A. G.

Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system. J. Sound Vibr., 1981, 77(3), 403–415.

Warburton

G. B.

Optimum absorber parameters for minimizing vibration response. Earthquake Engng and Structural Dynamics, 1981, 9, 251–262.

Randall

S. E.

Halsted

D. M.

Taylor

D. L.

Optimum vibration absorbers for linear damped systems. Trans. ASME J. Mech. Des., 1981, 103, 908–913.

10.

Jordanov

I. N.

Cheshankov

B. I.

Optimal design of linear and non-linear dynamic vibration absorbers. J. Sound Vibr., 1988, 123(1), 157–170.

11.

Ruzicka

J. E.

Passive shock isolation. J. Sound Vibr., August 1970, 14–24.

12.

Krasnicki

E. J.

The experimental performance of an ‘on/off’ active damper. Shock and Vibr. Bull., May 1981, 51(1), 125–131.

13.

Soliman

J. I.

Ismailzadeh

Optimization of undirectional viscous damped vibration isolation systems. J. Sound Vibr., 1974, 36(4), 527–539.

14.

Lizell

Semi-active damping. Proceedings of IMechE International Conference on Advanced suspensions, 1988, paper C429/88, pp. 83–91 (Mechanical Engineering Publications, London).

15.

Hennecke

Zieglmeier

F. J.

Frequency dependent variable suspension damping—theoretical background and practical success. Proceedings of IMechE International Conference on Advanced suspensions, 1988, paper C431/88, pp. 101–111 (Mechanical Engineering Publications, London).

16.

Hedrick

J. K.

Butsuen

Invariant properties of automotive suspension. Proceedings of IMechE International Conference on Advanced suspensions, 1988, paper C423/88, pp. 35–42 (Mechanical Engineering Publications, London).

17.

Craighead

I. A.

An active suspension system for an ambulance stretcher. Proceedings of IMechE International Conference on Advanced suspensions, 1988, paper C426/88 pp. 59–67 (Mechanical Engineering Publications, London).

18.

Popov

Sankar

Modelling and analysis of non-linear orifice type damping in vibration isolators. J. Sound Vibr., 1995, 183(5), 751–764.