On vibration transmission in oscillating systems incorporating bilinear stiffness and damping elements

This paper investigates the dynamic characteristics and vibration transmission behaviour of a single oscillator and also coupled oscillators incorporating both bilinear stiffness and bilinear damping elements. Both harmonic balance analytical approximations and numerical integrations are used to obtain the steady-state dynamic response and vibration transmission behaviour. Vibration transmission within the oscillating systems is evaluated by time-averaged power flow variables and force transmissibility. For the single oscillator with bilinear elements, it is shown that a small bilinear stiffness ratio is beneficial in the suppression of force transmission in the high-frequency range. A large bilinear damping ratio can reduce the peak force transmissibility and also the peak time-averaged input power. For the coupled oscillators with interfacial bilinear elements, it is also found that a small bilinear stiffness ratio can reduce both the force transmissibility and the time-averaged transmitted power at high excitation frequencies. A combination of a small bilinear stiffness ratio and a large bilinear damping ratio can lead to effective mitigation of vibration transmission in a wide range of excitation frequencies. It is also shown that the inclusion of bilinear elements may cause large superharmonic or subharmonic response components, which result in high vibration transmission level. These results provide a better understanding of the effects of bilinear stiffness and bilinear damping on vibration transmission, and benefit future designs of vibration suppression systems with such elements.