The isolation characteristics of an archetypal dynamical model with stable-quasi-zero-stiffness

• The exact motion equation of a model, based upon SD oscillator, with stable-quasi-zero-stiffness (SQZS) is studied.
• Analytical and numerical results for transmissibility including related comparisons are presented.
• The phenomena of chaos and bifurcation are revealed in frequency domain.
• A method avoiding multiple solutions to broaden isolation frequency band is proposed.

In this paper, a single-degree-of-freedom geometrically nonlinear oscillator with stable-quasi-zero-stiffness (SQZS) is presented, which can be extensively applied in vibration isolation due to its high static load bearing capacity and low dynamic stiffness. This model comprises a lumped mass denoeing the isolated object and a pair of horizontal springs providing negative stiffness paralleled with a vertical linear spring to bear the load. The equation of motion of the system is formulated with an originally irrational nonlinearity based upon SD oscillator instead of the conventionally approximate Duffing system of polynomial type, which will produce results with a high precision unquestionably, especially for the prediction of a large displacement behaviour. The frequency response characteristics particularly for transmissibility of the model, subjected to harmonic forcing and vibrating base, are obtained by using an extended averaging approach to achieve the parameter optimization for maximum frequency band of isolation. Furthermore, numerical simulations are carried out to detect the complex dynamical phenomena of periodic, chaotic motions and coexistence of multiple solutions, and so on, in addition to verifying the analytical results. Finally, an interesting strategy is proposed to extend the frequency band of isolation by controlling the initial value within the attraction basin of a small amplitude attractor, which can be utilized for an effective isolation. The results presented herein provide an insight of dynamics into the SQZS mechanism for its application in vibration engineering.