Bifurcation and dynamic analysis of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure

In order to guide the design of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure, the bifurcation and the chaos-occurring parameter region are investigated. The equilibrium point bifurcation with different load conditions and stiffness types is first obtained, and the invariant manifolds at specific parameters can be compared for four operating conditions based on a combination of two asymmetric stiffnesses and two mismatch loads. The displacement transmissibility and the direct current component of response are analyzed under these four operating conditions, and based on the results, it can be found that the four operating conditions can be divided into two categories, each with a similar pattern. Finally, the chaos-occurring parameter region is analyzed by means of largest Lyapunov exponent, and the maximum external excitation amplitude is used to indirectly evaluate the operation stability margin of these four operating conditions.