Modeling and analysis of folding rudder stiffness using spring elements to equivalently represent nonlinear elements

The mechanism and principles of the impact of nonlinear elements on the dynamic characteristics of the folding rudder structure under different states are investigated in this paper. A spring element dynamic modeling method is proposed, which uses uniformly distributed parallel spring elements to represent the contact stiffness nonlinearity caused by interface errors in the folding rudder. A stiffness simulation analysis model of the folding rudder under different states is established, and modal simulation analysis and experimental validation are conducted. The experimental validation results show that the relative error in the inherent frequency between the simulation analysis results and the experimental results for the folding rudder model under different states is less than 6%, indicating that the model can effectively replicate and predict the dynamic characteristics of the folding rudder. Therefore, a stiffness model that can accurately predict the dynamic characteristics of the folding rudder in different states is established. The results show that the inherent frequency of the folding rudder structure gradually increases with the increase in the equivalent stiffness of the spring elements and eventually stabilizes. Using the method of spring element equivalence to model the contact stiffness at the interface can effectively replicate the contact nonlinearity of the gaps in the folding rudder structure under different states. Moreover, increasing the number of equivalent springs on the contact surface improves the prediction accuracy of the folding rudder's dynamic characteristics.