Objective To address the challenge of predicting the shock response of shipboard equipment in an underwater explosion shock environment, this study conducts theoretical research on shock response prediction and shock-resistance performance optimization of nonlinear coupled vibration isolation systems, providing theoretical support for the shock-resistant design of such systems.

Method To accurately analyze the system response under underwater explosion shock loading, a theoretical shock dynamics model of a nonlinear coupled vibration isolation system is established, incorporating segmented-stiffness isolators, flexible pipes, and limiters under the dual-wave shock loading generated by an underwater explosion. Based on the Laplace transform and the residue method, a piecewise switching strategy is introduced to address the nonlinear stiffness characteristics. Analytical solutions for the shock displacement and acceleration responses of the system are derived and subsequently validated through comparisons with finite element numerical simulations and experimental results. On this basis, a multi-objective parameter optimization framework considering both displacement and acceleration responses is constructed using the Non-dominated Sorting Genetic Algorithm II (NSGA-II), enabling the optimization of the shock resistance performance of shipborne nonlinear vibration isolation systems.

Results The errors between the peak displacement and acceleration values predicted by the theoretical model and those obtained from numerical simulations and experimental measurements are all less than 10%, demonstrating the reliability and accuracy of the established theoretical model.

Conclusion Within the design ranges of the optimization variables determined from the existing typical ship component spectra, the parameter configurations optimized for displacement-priority and acceleration-priority scenarios achieve improvement rates of 37% and 6%, respectively. These findings provide a solid theoretical foundation and clear guidance for the shock-resistant design and performance optimization of nonlinear coupled vibration isolation systems under underwater explosion shock environments.