Exploiting Noise for Response Control: From Simple Nonlinear Systems to Slender Structures

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Random fluctuations, which are called noise, occur naturally in many systems, and in many biological and chemical systems, noise is utilized to engender a large change in the system response. However, the use of noise to beneficially influence the response of an engineering system has received only limited attention. As the operating environments of engineering systems become extreme, both at the small scales as well as the large scales, the influence of nonlinearities, uncertainties, and noise gain increased importance. The study, and possible exploitation, of these usually ignored elements may allow for breakthrough advances in design and control of systems and help extend the frontiers of engineering and science. Through support of this award, fundamental studies will be pursued to develop a knowledge base for the use of combined deterministic and noise inputs to realize desired response changes in nonlinear systems. A salient impact is expected to be the advancement of our understanding of noise based schemes for control of nonlinear systems and extension of the application realm of these schemes from simple systems to complex systems. By experimentally demonstrating the feasibility of these schemes, it is expected that one can construct schemes for practical applications where slender, rotating structures are used, such as drilling and mining operations and subtractive manufacturing operations such as milling operations. This work will usher in a new generation of researchers trained to use tools suited for nonlinear systems with noise.Building on prior efforts on noise-influenced responses of nonlinear oscillators and investigations into whirling motions of rotary systems carried out at the University of Maryland, a research team will pursue the common goal of understanding how mechanical and structural system responses may be altered by exercising partial control with noise. The group will conduct original experiments to explore the applicability of partial control schemes developed for Hénon maps and Duffing oscillators to an experimental prototype of a bi-stable Duffing oscillator. Informed by the experimental findings, analytical and numerical studies will be initiated with modified Jeffcott rotor systems to construct appropriate partial control algorithms and these findings will be extended to control the dynamics of slender, rotating structures. The findings are expected to open the doors to the combined use of noise and deterministic inputs for control of nonlinear mechanical systems that exhibit escape dynamics and steer responses of rotary systems away from states such as whirling motions, which can be detrimental to a system.