A frequency domain analysis of the effects of nonlinear damping on the Duffing equation

• The properties of nonlinearly damped Duffing systems are analysed theoretically.
• The Output Frequency Response Function concept is applied for the analysis.
• Nonlinear damping is more effective than linear damping in vibration isolation.
• Better vibration isolation can be achieved by both nonlinear damping and stiffness.

The nonlinearly damped Duffing equation has been studied using a variety of approximation and numerical methods by a number of authors. In this paper, the Duffing equation is examined analytically for the first time using the output frequency response function (OFRF) approach. The theoretical analysis focuses on the effects of the nonlinear stiffness and nonlinear damping on the output spectra as well as the output energy spectra over different frequency ranges. The studies reveal that nonlinear damping has two significant implications for the design of vibration isolation systems. First, nonlinear viscous damping is shown to be more effective in suppressing the resonant peak of a Duffing system than linear damping because the high frequency transmissibility is hardly affected. Second, nonlinear damping can be used in conjunction with nonlinear stiffness to achieve better vibration isolation. Simulation studies are also provided to validate and demonstrate these theoretical findings.