Article

Theoretical study of the effects of nonlinear viscous damping on vibration isolation of sdof systems

Journal of Sound and Vibration (Impact Factor: 1.86). 06/2009; 323(1-2):352-365. DOI: 10.1016/j.jsv.2009.01.001

ABSTRACT The present study is concerned with the theoretical analysis of the effects of nonlinear viscous damping on vibration isolation of single degree of freedom (sdof) systems. The concept of the output frequency response function (OFRF) recently proposed by the authors is applied to study how the transmissibility of a sdof vibration isolator depends on the parameter of a cubic viscous damping characteristic. The theoretical analysis reveals that the cubic nonlinear viscous damping can produce an ideal vibration isolation such that only the resonant region is modified by the damping and the non-resonant regions remain unaffected, regardless of the levels of damping applied to the system. Simulation study results demonstrate the validity and engineering significance of the analysis. This research work has significant implications for the analysis and design of viscously damped vibration isolators for a wide range of practical applications.

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    • "Nonlinear controllers are thus required for the control of a tone in these forms of nonlinearity, because the plant must be driven with a nonsinusoidal input to control the sinusoidal response – see, for example, Sutton and Elliott (1995). The response of a system with cubic damping to a sinusoidal excitation is, however, mainly sinusoidal (Lang et al., 2009; Laalej et al., 2012; Ghandchi Tehrani and Elliott, 2014; Elliott et al., 2015). Thus the vibration control of a system with nonlinear damping often does not require the use of a nonlinear controller. "
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    • "Although excellent low frequency isolation performance could be obtained through active isolation techniques, high energy cost, high development expense, actuation saturation, stability issues, and/or complexity in implementation etc. could occur. Alternatively, the semi-active control method can be employed to realize excellent vibration transmissibility at resonant frequency and above through some simple nonlinear damping systems [22] [23] [24] [25] [26]. But ultra-low frequency vibration control may still be a problem that cannot be addressed with pure damping control methods. "
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    ABSTRACT: This study presents some novel results about analysis and design of low-frequency or broadband-frequency vibration isolation using a hybrid lever-type isolation system with an X-shape supporting structure in passive or semi-active control manners. It is shown that the system has inherent nonlinear stiffness and damping properties due to structure geometrical nonlinearity. Theoretical analysis reveals that the hybrid isolation system can achieve very good ultra-low-frequency isolation through a significantly-improved anti-resonance frequency band (by designing structure parameters). Noticeably, the system can realize a uniformly-low broadband vibration transmissibility, which has never been reported before. Cases studies show that the system can work very well with good isolation performance subject to multi-tone and random excitations. The results provide a new innovative approach to passive or semi-active vibration control (e.g., via a simple linear stiffness control) for many engineering problems with better ultra-low/broadband-frequency vibration suppression.
    International Journal of Mechanical Sciences 04/2015; 98. DOI:10.1016/j.ijmecsci.2015.04.012 · 2.06 Impact Factor
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    • "Nonlinear controllers are thus required for the control of a tone in these forms of nonlinearity, because the plant must be driven with a nonsinusoidal input to control the sinusoidal response – see, for example, Sutton and Elliott (1995). The response of a system with cubic damping to a sinusoidal excitation is, however, mainly sinusoidal (Lang et al., 2009; Laalej et al., 2012; Ghandchi Tehrani and Elliott, 2014; Elliott et al., 2015). Thus the vibration control of a system with nonlinear damping often does not require the use of a nonlinear controller. "
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    ABSTRACT: In this study, an adaptive control system to reduce the tonal vibration of a mechanical system characterized by nonlinear damping is considered. Since the response of the system to a sinusoidal excitation is however mainly sinusoidal, nonlinear controllers are not required for the control of a tone in such a mechanical system. The adaptation and stability of an adaptive control algorithm, however, depends on the accuracy of the plant model. Since the tonal response of the nonlinear system changes with excitation level, conventional adaptive algorithms, with a fix linear model of the plant, can be slow to converge and may not achieve the desired performance. The use of an online observer is proposed, to estimate the describing function model of the plant, which will vary with excitation level. This allows the adaptive control algorithm to converge more quickly than using a fixed plant model, although care has to be taken to ensure that the dynamics of the observer do not interfere with the dynamics of the adaptive controller.
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