By changing the structure and parameters, the rectangular air spring can have an ideal ratio of vertical stiffness to lateral stiffness, which can satisfy the engineering requirements. Considering the nonlinearity of the rubber-cord composite material, the geometric nonlinear process caused by large deformation and the contact between the rigid base plate and the flexible capsule, a finite element model for the rectangular air spring was established, its vertical stiffness and lateral stiffness were calculated and their characteristic curves with different initial gas pressures, gas volumes, cord angles and number of cord layers were plotted. The influence of these factors on the air spring’s stiffness was analyzed. Finally, the reliability of the results of the finite element analysis was proved by the experimental testing.

An actual hybrid vibration isolation system usually consists of a rigid vibration source, a flexible base, an isolator and an actuator. It is a complex rigid-flexible coupled system with infinite dimensions. To obtain an accurate model and design the controller expediently, the hybrid vibration isolation system with flexible base is modeled based on the substructure modal synthesis method. The availability of this modeling method is proved in comparison with the FEM model built by ANSYS. Then, a hybrid vibration isolation control system is designed, simulated and analyzed based on the modified independent-modal space-control method. The results show that the vibration of the base is reduced effectively by the hybrid vibration isolation system, and the isolation effect is better than that of the passive vibration isolation system.

Usually, the stiffness of the conventional isolator is small because the performance of vibration isolation is preferential to that of shock isolation. This leads to high efficiency of shock isolation but large relative displacement. Moreover, the stiffness break is induced by the displacement restrictor, and the efficiency of shock isolation is deteriorated. Based on the law of conservation of energy, the conventional shock isolator and the Ruzicka isolator is modeled and analyzed, and the cushioning coefficients are obtained. Comparison shows that the Ruzicka isolator has more excellent performance than that of the conventional isolator. The shock isolation system with the Ruzicka isolator is changed to the dimensionless form with an acceleration pulse input of half sine shape. The shock response is calculated, and the parameters with high efficiency of shock isolation are obtained. The shock response shows that the maximal acceleration and relative displacement are restricted below the limit value by the Ruzicka isolator when the conventional design fails to protect the object.

Considering force transmissibility and the magnitude of actuator output, an optimal control is applied to a double-layer vibration isolation system. The relationship between the weighting matrix and the feedback matrix is acquired. The transfer function of output performance versus input disturbance is obtained. By analyzing the amplitude and frequency characteristics of the transfer function, the affect of the weighting matrices Q and R on the system characteristics is found. Thus, the weighting function can be reasonably selected. The optimal design of the controller can be realized with the consideration of various performance objectives.

A new method that can apply DDAM to nonlinear stiffness system is put forward in the paper, an equivalent linear stiffness model with displacement restrictor is constructed, and the optimal scheme is designed. Pareto setting is obtained by finite element method and genetic algorithm, this pareto setting would be an excellent reference for engineering application. This design mode would assure excellent vibration and shock isolation at the same time, that is significative for vibration and shock isolation of onboard settings.