The modal perturbation method(MPM) is a modal truncation technique based on matrix norms, applicable to complex dynamic systems in engineering, physics, mathematics, and related fields. This method is grounded in modal analysis theory, using the modal characteristics of an unperturbed state as a basis and introducing small parameter perturbations to iteratively solve the system’s linear and nonlinear stiffness matrices, thereby quantifying the relative error between adjacent systems. The core idea is to leverage the properties of small parameters to transform a high-dimensional complex system into an equivalent low-dimensional system, achieving model order reduction and efficient computation. The key steps of the method include: first, identifying low-order modes that significantly influence structural dynamic behavior to construct a simplified initial model; second, refining the modes based on perturbation theory; and finally, progressively screening critical modes that contribute substantially to the system by computing the norm of the stiffness matrix. The advantages of the MPM lie in its ability to simplify complex modal analysis problems using fundamental mathematical theory, offering high computational accuracy and broad applicability. However, the method imposes certain requirements on the selection of small parameters, and it may incur higher computational costs under large perturbations. Compared with the Galerkin method, the MPM can achieve the accuracy of the 11th-order Galerkin method with only a few modes when dealing with the modal truncation of cables under parametric excitation, and the calculation efficiency is significantly improved.