Critical criterion of amplitude death stability in multi-modular floating systems with multi-frequency excitations

In coupled modular floating systems, amplitude death (AD) denotes a suppressed dynamic state characterized by the cessation of oscillatory activity. This study derives analytical solutions for AD and establishes its critical conditions under multi-frequency excitations. We demonstrate that AD is modulated by harmonic functions determined by the excitation frequencies, enabling the formulation of a fundamental solution for the AD state. Employing the harmonic balance method, this solution is obtained by resolving coefficients within a system of nonlinear algebraic equations. The derived analytical solution elucidates the distribution of AD states within the parameter design space, offering critical insights for system stability design. Furthermore, a generalized critical criterion is established, delineating the parametric boundaries governing the emergence and cessation of AD. Theoretical predictions demonstrate strong concordance with numerical simulations. As a practical application, the stability design of modular floating airports is investigated, leveraging the AD mechanism to enhance structural resilience under dynamic loading. This work provides a foundational framework for optimizing stability in complex floating systems subjected to multi-frequency environmental forces.