Dynamics and isolation properties for a pneumatic near-zero frequency vibration isolator with nonlinear stiffness and damping

Aiming to isolate disturbance vibration for heavy machines with low frequency, a novel hydro-pneumatic vibration isolator with high-static and low-dynamic (HSLD) stiffness is proposed, which contains bellows structure as elastic element and pressurized gas and incompressible liquid as working media. Due to that the natural frequency of isolation system with such isolator is close to zero and loading capacity can be adjusted by the gas pressure, the proposed device is termed as pneumatic near-zero frequency (NZF) vibration isolator. To obtain the mathematical model of isolator’s stiffness, the quasi-static derivation based on gas state equation is carried out first. Results prove that the presented isolator possesses ideal high-static and low-dynamic stiffness, which is also verified by the experimental data measured by a quasi-static test. The proportion of gas volume to total volume of gas and liquid media, respectively, in bellows and cylinder chambers are significant physical parameters, which dominate the nonlinearity extent of isolator’s stiffness. Different from most existing isolators, the proposed isolator includes fluidic damping and friction damping. The former is expressed by classic square-velocity-type nonlinear model, and the latter is modeled as Coulomb damping. To obtain dynamic response and vibration isolation transmissibility, the harmonic balance method is applied. A direct current term is added in the trial solution, which reflects the asymmetry of dynamic response. In respect of transmissibility analysis, square-velocity nonlinear damping brings a favorable advantage that it can ensure the fine force transmissibility in both resonance region and effective isolation band. This conclusion holds consistently under base motion excitation. Friction damping cannot give the same conclusion. Further comparison with a linear vibration isolator exhibits that the HSLD stiffness characteristics of the NZF isolator breaks through the trade-off between large loading capacity and small static deformation, and the square nonlinearity of fluid damping is able to overcome the dilemma that weak linear vicious damping is beneficial for isolation performance within the effective isolation frequency band, but cannot suppress resonance amplitude and transmissibility. And the experimental transmissibility is in good agreement with the analytical result. Besides, the influences of excitation variation on isolation performance are estimated theoretically. Due to the hardening stiffness, overload acceleration will cause the increase in linearized natural frequency of NZF isolator system, and thus, isolation effectiveness will be reduced.