The effects of cubic damping on vibration isolation

Abstract

Vibration isolators are often assumed to possess linear viscous damping which has well known consequences for their performance. However, damping may be designed to be or prove to be nonlinear. This study investigates the effect of cubic damping, as an example of damping nonlinearity, in a single degree of freedom (SDOF) vibration isolation system. The response behaviour due to two excitation types, namely harmonic and broadband excitations, was examined.

For harmonic excitation, the Harmonic Balance Method (HBM) was applied to yield approximate closed form solutions and simplified analytical expressions implicitly show the influence of cubic damping for particular frequency regions. The HBM solutions were verified using direct numerical integration. The presence of cubic damping proves to be beneficial for the force excited case. It reduces response amplitude around the resonance frequency and has similar response to an undamped system in the isolation region. In contrast, for base excitation, the cubic damping is detrimental at high excitation frequencies as the base excitation and isolated mass move almost together. The effect becomes more pronounced for larger excitation amplitudes.

The case of base excitation was then considered for broadband excitation. The responses using direct numerical integration were presented using power spectral densities. In contrast to harmonic excitation, the amplitude of the response does not appear to approach that of the input. Instead, a higher effective cubic damping results in a higher vibration level of the isolated mass at frequencies below the resonance frequency. It also does not reduce explicitly the response amplitude around the resonance frequency unlike the linear viscous damping. For a constant displacement amplitude random excitation, the excitation frequency bandwidth is found to be a significant factor in the level of effective cubic damping. A broader excitation bandwidth results in a higher level of cubic damping force.

The theoretical and numerical results for both harmonic and broadband excitation were validated experimentally. The experimental investigation was performed using a SDOF base excited vibration isolation system possessing a simple velocity feedback control active damper to reproduce the nonlinear damping force. The predictions were shown to be in good agreement with measurements thereby verifying the effects of cubic damping on a SDOF system undergoing harmonic and broadband base excitation.

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ORCID for N.S. Ferguson: orcid.org/0000-0001-5955-7477

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