Stability and Robustness Analysis of Quasi-Periodic System subjected to Uncertain Parametric Excitations and Nonlinear Perturbations

IF 1.9 4区工程技术 Q2 ACOUSTICS

Journal of Vibration and Acoustics-Transactions of the Asme Pub Date : 2022-04-18 DOI:10.1115/1.4054359

Susheelkumar Cherangara Subramanian, S. Redkar

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引用次数: 0

Abstract

In this work, the asymptotic stability bounds are identified for a class of linear quasi-periodic dynamical systems with stochastic parametric excitations and nonlinear perturbations. The application of a Lyapunov-Perron (L-P) transformation converts the linear part of such systems to a linear time-invariant form. In the past, using the Infante approach for linear time-invariant systems, stability theorem and corollary were derived and demonstrated for time periodic systems with variation in stochastic parameters. In this work, the same is extended towards linear quasi-periodic with stochastic parameter variations. Furthermore, the Lyapunov's direct approach is employed to formulate the stability conditions for quasi-periodic system with nonlinear perturbations. If the nonlinearities satisfy a bounding condition, sufficient conditions for asymptotic stability are derived for such systems. The application of both derived stability theorems are demonstrated with practical examples of commutative and non-commutative quasi-periodic systems.

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不确定参数激励和非线性扰动下拟周期系统的稳定性和鲁棒性分析

本文研究了一类具有随机参数激励和非线性扰动的线性拟周期动力系统的渐近稳定界。Lyapunov-Perron (L-P)变换的应用将这种系统的线性部分转化为线性定常形式。过去，对于线性定常系统，利用Infante方法推导并证明了随机参数变化的时间周期系统的稳定性定理和推论。在这项工作中，同样的扩展到具有随机参数变化的线性拟周期。在此基础上，利用Lyapunov直接方法给出了具有非线性扰动的拟周期系统的稳定性条件。如果非线性满足边界条件，则得到了系统渐近稳定的充分条件。通过可交换和非可交换拟周期系统的实例，证明了所导出的稳定性定理的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Vibration and Acoustics-Transactions of the Asme 工程技术-工程：机械

CiteScore

4.20

自引率

11.80%

发文量

审稿时长

7 months

期刊介绍： The Journal of Vibration and Acoustics is sponsored jointly by the Design Engineering and the Noise Control and Acoustics Divisions of ASME. The Journal is the premier international venue for publication of original research concerning mechanical vibration and sound. Our mission is to serve researchers and practitioners who seek cutting-edge theories and computational and experimental methods that advance these fields. Our published studies reveal how mechanical vibration and sound impact the design and performance of engineered devices and structures and how to control their negative influences. Vibration of continuous and discrete dynamical systems; Linear and nonlinear vibrations; Random vibrations; Wave propagation; Modal analysis; Mechanical signature analysis; Structural dynamics and control; Vibration energy harvesting; Vibration suppression; Vibration isolation; Passive and active damping; Machinery dynamics; Rotor dynamics; Acoustic emission; Noise control; Machinery noise; Structural acoustics; Fluid-structure interaction; Aeroelasticity; Flow-induced vibration and noise.