Nonlinear primary responses of a bilateral supported X-shape vibration reduction structure

Abstract

The nonlinear forced vibration responses of a bilateral supported X-shape vibration reduction structure are researched. The vertical and rotational displacements of the upper and lower platforms of the structure are taken into account and the nonlinear dynamic model of the structure with four degrees of freedom is established by applying the Lagrange’s equation. The validate experimental study of the structure is carried out and the acceleration response measured from the experiment is compared with the numerical result to verify the correctness of the dynamic model. The steady state amplitude-frequency responses of the system are obtained via the incremental harmonic balance (IHB) method and validated by using the Runge-Kutta numerical simulation. From the analysis, it can be seen that the primary responses of the vertical and rotational displacements of the structure exhibit softening type of nonlinearity. The coupled resonance of the vertical and the rotational displacements of the system can be observed when the system resonances around the fundamental and second natural frequencies. Besides, parametric investigations are performed to analyze the effects of the viscous damping coefficient, the external excitation amplitude, the angle between the rod and the platform, and the stiffness coefficient of the support spring on the resonance properties of the X-shape vibration reduction structure.