论文标题
减少受外部激发的非线性准周期系统
Order Reduction of Nonlinear Quasi-periodic Systems Subjected to External Excitations
论文作者
论文摘要
在他的论文中，我们介绍了受外部激发的非线性准周期系统的订单减少技术。此处介绍的降级技术基于Lyapunov-渗透（L-P）的转换。对于一类非谐振的准周期系统，L-P变换可以将线性准周期系统转换为线性时间不变的系统。该线性时间不变（LTI）系统保留了原始的准周期系统的动力学。一旦获得了LTI系统，就可以使用可用于分析LTI系统的工具和技术，并且可以通过L-P变换为原始的准周期系统获得结果。这种方法类似于使用Lyapunov-Floquet（L-F）转换将线性时间周期系统转换为LTI系统并执行分析和控制。 减少订单是一种系统的方式，可以使用相对较小的状态构建动态系统模型，该模型准确地保留了大规模系统的基本动力学。在这项工作中，介绍了受外部激发的非线性准周期系统的减少级建模技术。这里提出的方法使用L-P变换，该L-P变换使转换方程的线性部分具有时间不变。在这项工作中，建议了两种减少技术。第一种方法只是将众所周知的圭亚人（例如还原方法）应用于非线性系统。第二种技术是基于准周期系统不变歧管的概念。 基于“准周期性不变歧管”的技术产生了“降低性条件”。这些条件有助于我们了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，非线性和外部激发之间的能量相互作用。
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.
