Analyzing and Exploiting Hybrid Dynamical Systems Containing Piecewise Linear Nonlinearities

该项目将通过支持研究来促进国家利益，这些研究将改进各种工程系统的设计过程，这些系统中组件之间的摩擦和间歇性接触会显著影响性能。这些系统包括飞机发动机和涡轮机械的阻尼装置，以及提供绿色能源的水浮标等能量收集器。目前的技术无法预测这些复杂系统的响应，因此阻碍了新技术的发展。这项研究将为推进下一代阻尼装置和能量收集器的设计过程提供新技术。优化的阻尼器设计将解决严重的疲劳问题，并降低飞行飞行器和涡轮机械所需的维护成本。这项研究还将创造一种新的能量收集方法，将提供更好的发电效率。这项研究将与教育组成部分相结合，将工作传播给本科生和幼儿园到八年级的代表性不足的群体，以帮助扩大参与研究并积极影响工程教育。由于缺乏计算效率和现有方法分析诱导的分段线性非线性的能力有限，具有干摩擦和/或间歇接触的复杂系统的动力学预测和开发具有挑战性。这项研究将创造一种新的有效技术，使大型分段线性非线性系统的瞬态和稳态响应的计算成为可能，从而分析、监测和控制它们的动力学。这项研究有三个主要目标。首先，建立了一种计算分段线性非线性复杂系统时域响应的方法。该项目的方法能够分析这些系统的任何类型的响应（例如，周期、准周期和混沌响应）。其次，当大型分段线性非线性系统周期性响应时，创建一种快速近似稳态振动幅值和频率的方法。该方法将使这些系统的参数和统计研究以及新的振动控制策略成为可能。第三，将一般方法应用于两个实际应用：含非线性阻尼的涡轮机械分析和改善能量采集器振动性能的主动间隙控制。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will advance national interests by supporting research that will improve the design process of a variety of engineered systems where rubbing and intermittent contact between components significantly affects performance. These systems include damping devices for aircraft engines and turbomachinery, and energy harvesters such as water buoys that provide green energy. Current techniques are not able to predict the response of these complex systems and hence obstruct the development of new technologies. This research will provide new techniques to advance the design process of next-generation damping devices and energy harvesters. The optimal damper design will address serious fatigue problems and reduce required maintenance costs for flight vehicles and turbomachinery. This research will also create a new class of energy harvesting methods that will provide better power generation efficiency. The research will be integrated with an educational component disseminating the work to undergraduates and kindergarten through eighth grade underrepresented groups to help broaden participation in research and positively impact engineering education.Prediction and exploitation of the dynamics of complex systems with dry friction and/or intermittent contact is challenging due to the lack of computational efficiency and limited capability of current methods to analyze the induced piecewise-linear nonlinearities. This research will create a new class of effective techniques to enable the computation of the responses, both transient and steady-state, of large piecewise-linear nonlinear systems in order to analyze, monitor and control their dynamics. This research has three main goals. First, create a method to compute the time-domain response of complex systems with piecewise-linear nonlinearities. The project's approach enables the analysis of any type of response (e.g., periodic, quasi-periodic, and chaotic responses) of these systems. Second, create a method to rapidly approximate the steady-state vibration amplitudes and frequencies of large piecewise-linear nonlinear systems when they respond periodically. Parametric and statistical studies and new vibration control strategies of these systems will be enabled with this method. Third, apply the general methods to two real-world applications: the analysis of turbomachinery containing nonlinear damping and the active gap control for improved vibration performance of energy harvesters.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.