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Suppressing Resonant Vibrations Using Nonlinear Springs and Dampers

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

Stephen A. Billings

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK, s.billings{at}sheffield.ac.uk

Zi-Qiang Lang

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

Geoffrey R. Tomlinson

Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

The transmitted force around the resonant region of a system can be significantly reduced by introducing designed nonlinearities into the system. The basic choice of the nonlinearity can be either a nonlinear spring element or a nonlinear damping element. A numerical algorithm to compute and compare the transmitted force reduction produced by these two types of designed elements is proposed in this study. Analytical results are used to demonstrate the procedure. The numerical results indicate that the designed nonlinear damping element produces low levels of higher-order harmonics and no bifurcations in the system output response. In contrast, the nonlinear spring-based designs induce significant levels of harmonics in the transmitted force and can produce bifurcation behaviour. The conclusions provide an important basis for the design of nonlinear materials and nonlinear engineering systems.

Key Words: Energy transfer • damping • vibration transmissibility • harmonic balance method.

This version was published on November 1, 2009

Journal of Vibration and Control, Vol. 15, No. 11, 1731-1744 (2009)
DOI: 10.1177/1077546309102668


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