Over the last two decades, stochastic resonance, a nonlinear phenomenon in which the addition of noise to a stochastic system leads to a coherently amplified response, has been explored to explain the dynamics of systems ranging from the Earth?s climate to sensory neurons in a monkey?s ear. Although considerable work has been carried out in the context of physical and biological systems, the use of noise for the benefit of nonlinear mechanical and structural systems, in particular, their transduction properties, has not been widely explored. This is to be addressed here by developing a fundamental understanding of the phenomenon of stochastic resonance in coupled, nonlinear mechanical and structural systems, and use this understanding to develop novel mechanical and structural design methodologies that incorporate the advantages of stochastic resonance for enhancement of the mechanical transduction capabilities and signal detection capabilities of these systems. It is expected that this understanding will help use noise in a constructive manner in the design of nonlinear systems.
From a fundamental standpoint, as stochastic resonance is relevant to physical systems (periodic recurrences of ice ages, ring lasers, Schmitt triggers, optical devices, magnetic systems), chemical systems, and biological systems (sensory neurons), the findings of this study are expected to be important for a wide range of nonlinear systems including many outside mechanical and structural systems. For example, certain aspects of the study will carry implications for frontier research areas such as quantum metrology and quantum computation. From an application standpoint, the extension of the advantages of stochastic resonance in resonator arrays to the micro-scale and nano-scale can produce commercial benefits in the areas of sensing technologies and nanodevices. Finally, the application of stochastic resonance in nano-scale science to specific problems in a systematic manner is expected to be important for the education of future generations of students.
Many systems ranging from the Earth’s climate to sensory neurons in a monkey’s ear have required considerations of random or stochastic fluctuations called noise, whose introduction into a system is known to amplify system response. The associated phenomenon is often referred to as stochastic resonance. Considerable work has been carried out in the context of physical and biological systems and the beneficial effects of noise for these systems are well recognized. However, the situation is quite different in the context of mechanical and structural systems. Noise is often considered as being undesirable for these systems, and the use of noise for the benefit of nonlinear mechanical and structural systems, in particular, their response and performance characteristics has not received considerable attention. A multi-year effort has been pursued by a group of researchers from the University of Maryland. This group includes a faculty member from Mechanical Engineering and Applied Mathematics and Scientific Computation, undergraduate and graduate students from Mechanical Engineering, and a post-doctoral researcher. Through a combination of experimental, analytical, and numerical studies, the researchers have strived to further our understanding of noise-influenced behavior of nonlinear systems including coupled oscillator systems. The findings of this original work, which have been disseminated through peer reviewed journal articles, book chapters, and international conference presentations and publications, are illustrative of noise-facilitated energy localization, energy transfer, response sustainment, and response amplification and illuminate new possibilities for taking advantage of noise. These findings can serve as a platform to develop novel methodologies, which incorporate the benefits of noise for a range of micro-scale to macro-scale systems including sensing systems, transduction systems, and communication systems. In addition, noise may be used to benefit in systems with contact interactions to facilitate grazing type of contact or remove sticking contact. The analytical-numerical framework developed in this work can be used as a tool to examine the response of a wide variety of systems ranging from micro-scale to macro-scale systems. The experimental prototypes of nonlinear oscillators developed in this work have been and are being used in a graduate course related demonstrations. In addition, these prototypes have been used to illustrate complex and fascinating behavior exhibited by nonlinear systems to visitors from government laboratories, academia, and local schools. The undergraduate student involved in the research activity proceeded to pursue graduate studies with the principal investigator on a different nonlinear system and completed his Master of Science studies in Mechanical Engineering. The post-doctoral researcher assumed a research faculty position after his involvement in this work and he has continued to be active in this line of research. A Native American doctoral student involved in this research activity is currently a doctoral candidate in Mechanical Engineering, and he is on course to complete his doctoral studies in 2015.
