Analyzing and Exploiting Hybrid Dynamical Systems Containing Piecewise Linear Nonlinearities

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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.