标题： 非周期外部激励作用下非线性准周期系统的降阶 显示英文标题

标题： Order Reduction of Nonlinear Quasi-periodic Systems Subjected to External Excitations

摘要： 在他的论文中，我们提出了用于受外部激励的非线性准周期系统的降阶技术。 这里提出的降阶技术基于Lyapunov-Perrone（L-P）变换。 对于一类非共振的准周期系统，L-P变换可以将一个线性准周期系统转换为线性时不变系统。 这个线性时不变（LTI）系统保留了原始准周期系统的动力学特性。 一旦获得这个LTI系统，就可以使用可用于LTI系统分析的工具和技术，并通过L-P变换得到原始准周期系统的相关结果。 这种方法类似于使用Lyapunov-Floquet（L-F）变换将线性时变系统转换为LTI系统并进行分析和控制。 降阶是一种系统地构建具有相对较少状态的动力学系统模型的方法，这些模型能够准确保留大规模系统的本质动力学。 在这项工作中，提出了用于受外部激励的非线性准周期系统的降阶建模技术。 这里提出的方法使用L-P变换，使变换后的方程的线性部分变为时不变的。 在这项工作中，提出了两种降阶技术。 第一种方法只是将众所周知的Guyan类似降阶方法应用于非线性系统。 第二种技术基于准周期系统的不变流形概念。 基于“准周期不变流形”的技术产生“可降阶条件”。 这些条件有助于我们理解系统中各种类型的共振相互作用。 这些共振表明系统状态、非线性和外部激励之间的能量相互作用。 显示英文摘要

摘要： In his paper, we present order reduction techniques for nonlinear quasi-periodic systems subjected to external excitations. The order reduction techniques presented here are based on the Lyapunov-Perrone (L-P) Transformation. For a class of non-resonant quasi-periodic systems, the L-P transformation can convert a linear quasi-periodic system into a linear time-invariant one. This Linear Time-Invariant (LTI) system retains the dynamics of the original quasi-periodic system. Once this LTI system is obtained, the tools and techniques available for analysis of LTI systems can be used, and the results could be obtained for the original quasi-periodic system via the L-P transformation. This approach is similar to using the Lyapunov-Floquet (L-F) transformation to convert a linear time-periodic system into an LTI system and perform analysis and control. Order reduction is a systematic way of constructing dynamical system models with relatively smaller states that accurately retain large-scale systems' essential dynamics. In this work, reduced-order modeling techniques for nonlinear quasi-periodic systems subjected to external excitations are presented. The methods proposed here use the L-P transformation that makes the linear part of transformed equations time-invariant. In this work, two order reduction techniques are suggested. The first method is simply an application of the well-known Guyan like reduction method to nonlinear systems. The second technique is based on the concept of an invariant manifold for quasi-periodic systems. The 'quasi-periodic invariant manifold' based technique yields' reducibility conditions.' These conditions help us to understand the various types of resonant interactions in the system. These resonances indicate energy interactions between the system states, nonlinearity, and external excitation.