Dynamic modelling and analysis of nonlinear stiffness metamaterial isolators for underwater vehicles

This study presents a dynamic modelling and analysis method for metamaterial vibration isolation systems with nonlinear stiffness characteristics to address vibration control requirements in underwater vehicle propulsion systems. A metamaterial isolator is constructed based on the curved beam cell. An elastic force model is derived by formulating the nonlinear stiffness fitting relationship. The influences of the cell geometric parameters on the nonlinear stiffness coefficient are analyzed. The nonlinear stiffness model is incorporated into the system to establish a nonlinear single-degree-of-freedom (SDOF) dynamic model that accounts for the placement of the isolators. A test is used to validate the proposed model. A parameter design method for the isolators based on a nonlinear model is proposed, where the parameter combination is determined through dynamic response analysis. The validity of this isolator design method is confirmed by the simulation analysis. Research results indicate that with the fixed linear stiffness component, the proposed vibration isolator can decrease the force transmissibility response amplitude by about 25.8% relative to that of the conventional linear vibration isolator. The proposed design methodology can provide a theoretical basis for the applications of nonlinear metamaterial isolators.