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We model different nonlinear systems, analyze their nonlinear aspects and discuss their applications.
First, we present a semi-analytical, geometrically-exact, unsteady potential flow model is developed for airfoils undergoing large amplitude maneuvers. Towards this objective, the classical unsteady theory of Theodorsen is revisited by relaxing some of the major assumptions such as (1) flat wake, (2) small angle of attack, (3) small disturbances to the mean flow components, and (4) time-invariant free-stream. The kinematics of the wake vortices is simulated numerically while the wake and bound circulation distribution and, consequently, the associated pressure distribution are determined analytically. The steady and unsteady behaviors of the developed model are validated against experimental and computational results. The model is then used to determine the lift frequency response at different mean angles of attack.
Second, we investigate the nonlinear characteristics of an autoparametric vibration system. This system consists of a base structure and a cantilever beam with a tip mass. The dynamic equations for the system are derived using the extended Hamilton's principle. The method of multiple scales is then used to analytically determine the stability and bifurcation of the system. The effects of the amplitude and frequency of the external force, the damping coefficient and frequency of the attached cantilever beam and the tip mass on the nonlinear responses of the system are determined. As an application, the concept of energy harvesting based on the autoparametric vibration system consisting of a base structure subjected to the external force and a cantilever beam with a tip mass is evaluated. Piezoelectric sheets are attached to the cantilever beam to convert the vibrations of the base structure into electrical energy. The coupled nonlinear distributed-parameter model is developed and analyzed. The effects of the electrical load resistance on the global frequency and damping ratio of the cantilever beam are analyzed by linearizion of the governing equations and perturbation method. Nonlinear analysis is performed to investigate the impacts of external force and load resistance on the response of the harvester.
Finally, the concept of harvesting energy from ambient and galloping vibrations of a bluff body is investigated. A piezoelectric transducer is attached to the transverse degree of freedom of the body in order to convert the vibration energy to electrical power. A coupled nonlinear distributed-parameter model is developed that takes into consideration the galloping force and moment nonlinearities and the base excitation effects. The aerodynamic loads are modeled using the quasi-steady approximation. Linear analysis is performed to determine the effects of the electrical load resistance and wind speed on the global damping and frequency of the harvester as well as on the onset of instability. Then, nonlinear analysis is performed to investigate the impact of the base acceleration, wind speed, and electrical load resistance on the performance of the harvester and the associated nonlinear phenomena. Short- and open-circuit configurations for different wind speeds and base accelerations are assessed. |
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