A symmetrically piecewise linear oscillator: Design and measurement

Abstract

A simple piecewise linear system with symmetrical flexible constraints was designed and manufactured to carry out a wide range of experimental dynamic analysis and ultimately to validate piecewise models. The design choice was based on the following criteria: accuracy in representing the mathematical model, manufacturing simplicity, flexibility in terms of parameter changes and cost effectiveness. The system consists of a block mass attached to two leaf springs, the stiffness of which can easily be varied by changing their length. The secondary stiffness in the form of cantilever beams can be widely varied in the same way. The clearance between the mass and secondary springs can also be varied by adjusting the screws at the ends of the beams. A variable pneumatic damper is mounted on the upper surface of the mass and provides a means of changing the viscous damping coefficient. The experimental set-up, calibration procedures and typical results are discussed.

Keywords

piecewise oscillator non-linear dynamics design measurements

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References

Kobrynskii

A. E.

Dynamics of Mechanisms with Elastic Connections and Impact Systems, 1969 (Iliffle Books Limited, London).

Shaw

S. W.

Holmes

P. J.

A periodically forced piece-wise linear oscillator. J. Sound Vibr., 1983, 90(1), 129–155.

Nordmark

A. B.

Non-periodic motion caused by grazing incidence in an impact oscillator. J. Sound Vibr., 1991, 145(2), 279–287.

Peterka

Vacik

Transition to chaotic motion in mechanical systems with impacts. J. Sound Vibr., 1992, 154(1), 95–115.

Budd

Dux

Chattering and related behaviour in impact oscillators. Phil. Trans. R. Soc. Lond., 1994, 347, 365–389.

Wiercigroch

Bifurcation analysis of harmonically excited linear oscillator with clearance. Chaos, Solitons and Fractals, 1994, 4(2), 297–303.

Wiercigroch

Dynamics of Discrete Mechanical Systems with Discontinuities (in Polish), 1994 (Silesian University Press, Gliwice).

Wiercigroch

On modelling discontinuities in dynamic systems. Mach. Vibr., 1996, 5, 112–119.

Shaw

S. W.

Forced vibrations of a beam with one-sided amplitude constraint: Theory and experiment. J. Sound Vibr., 1985, 99(2), 199–212.

10.

Stenson

Nordmark

A. B.

Experimental investigations of some consequences of low impacts in the chaotic dynamics of mechanical system. Phil. Trans. R. Soc. Lond., 1994, 347, 439–448.

11.

Wiercigroch

Sin

W. T. V.

Measurement of chaotic vibration in symmetrically piecewise linear oscillator. Chaos, Solitons and Fractals, 1998, 9(1-2), 209–220.

12.

Wiercigroch

Sin

W. T. V.

Experimental study of based excited symmetrically piecewise linear oscillator. Trans. ASME, J. Appl. Mechanics, 1998, 65, 657–663.