On the dynamic behavior of the Zener model with nonlinear stiffness for harmonic vibration isolation

In this paper, the dynamic behaviour of a mechanical isolator known as the Zener model is considered. This model consists of a mass supported by a spring that is in parallel with two further elements in series; a damper and a second spring. Previous work had already demonstrated that this system has benefits for the transmissibility above the resonance frequency, when compared with the traditional spring-damper isolator. In this work we study the influence of replacing the main spring with a nonlinear cubic spring. In fact, we show that use of a cubic stiffness can provide improvement in the transmissibility for frequencies around and above the resonance if the stiffness is of the softening type. Results are based on the analytical development of the equation of motion using the harmonic balance method.