mems.seminar series

Abstract: Most current system interrogation approaches used in applications such as system identification, damage detection and structural health monitoring are passive in that they are based on passively observing the system dynamics. Other approaches are active in that they apply an auxiliary signal to the system (in the form of excitation). All such current techniques use predefined excitation signals, which can be of a variety of types, ranging from pulsed waves to frequency sweeps. Such auxiliary signals are designed off-line, and do not adapt to the particularities of the response of the system during its interrogation. A novel technique for interrogating systems by using nonlinear feedback auxiliary signals will be presented. The feedback nature of this form of excitation is an essential enabling feature for enhancing sensitivity and selectivity of the resulting novel interrogation paradigm. The proposed techniques are applied to sensing and damage detection, and exploit two radically new ideas.

The first idea is to actively induce desired nonlinear phenomena such as chaos and bifurcations in the dynamics of a system (which can be linear or nonlinear) by applying nonlinear feedback auxiliary signals. The morphology of bifurcation boundaries is then utilized to identify parameter variations indicative of damage. Moreover, the morphology (deformation) of the attractor of the nonlinear closed loop dynamics is used to identify multiple simultaneous parameter variations (e.g. damages) with very high sensitivity by employing a novel concept referred to as sensitivity vector fields. A unique perspective on the design of suitable attractors by means of nonlinear feedback auxiliary signals is discussed. In particular, the question of how to design a nonlinear controller that creates an attractor whose morphing reveals certain parameter variations most effectively is tackled. Most current studies of such problems are based on linear theories. In contrast, the proposed approaches exploit nonlinear phenomena, and can enhance accuracy and sensitivity (e.g. by monitoring attractor morphing).

The second key idea is based on a novel methodology for designing optimal nonlinear controllers for system interrogation. To design such controllers, the nonlinearity is accounted for by creating augmented linear models of higher order (in a higher dimensional state space). These augmented models have a specific forcing in the augmented degrees of freedom. The specific forcing ensures that the augmented models follow the trajectory of the nonlinear system when projected onto the original (physical) space. These augmented models open the door to using advanced (input/output) approaches for modal extraction and system identification which previously could be used only for linear systems. The input/output nature of the identification approach is particularly well suited for use in conjunction with nonlinear feedback auxiliary signals since there the input excitation is known (as the controller output is easily measured). This technique addresses three major limitations of existent frequency-based detection methods, namely the low sensitivity of the frequencies to damages, the limited number of parameters identifiable from frequency-only measurement data, and the need for enhanced sensitivity for nonlinear systems.

To demonstrate the applicability and the potential offered by the proposed approach, several systems are explored numerically and experimentally, including various frame structures, a cantilever sensing beam, and an atomic force microscope in tapping mode.

Professor Bogdan Epureanu received his Ph.D. in Mechanical Engineering from Duke University in 1999, where he worked under the supervision of Professors Earl Dowell and Kenneth Hall. He is now with the University of Michigan in Ann Arbor, where his research interests focus on nonlinear mechanical phenomena with applications to structural health monitoring, sensors, fluid-structure interactions (aeroelasticity, unsteady aerodynamics), and nanoscale problems in bio-dynamics. Among his honors, Professor Epureanu received the 2004 American Academy of Mechanics Junior Achievement Award, an NSF Career Award in 2004, the 2003 ASME/Pi Tau Sigma Gold Medal Award from the engineering honor society and the ASME, the 2001 Young Innovator Award from Petro-Canada, and was the winner of Eaton Corporation's 1999 International Mechanical Design Contest. In 1998, Professor Epureanu received the A. M. Strickland Award from the Institution of Mechanical Engineers' Division of Manufacturing Industries. Recently, he has been awarded the Ferdinand Beer and R. Johnston Outstanding Mechanics Educator Award by the American Society for Engineering Education (ASEE - Mechanics Division).

Abstract: As we enter the age of robotic and intelligent machines, it is useful to review the historical role of dynamics in the invention and creation of machines. In this lecture we review the dynamical ideas, constructs and principles of importance to machine designers from Leonardo da Vinci and the Renaissance engineers to the machine age of 19th and early 20th century. One of the themes of this lecture is the time lag between mathematical analysis in dynamics and its application to the design of machines. The rise of kinematics of machines in the 19th C. and Franz Reuleaux's theory of machines is reviewed. The use of dynamical theory in machine did not see significant use until the early 20th C. in the works of Timoshenko and other Russian mechanicians as well as Den Hartog. Likewise today we see a lag in the use of control theory in machines and mechatronics application. We also review the role of nonlinear dynamics and stability analysis in machines from Maxwell's analysis of steam engine regulators to the modern role of chaotic dynamics in understanding the origins of machine noise. An example of chaos in clock escapements will be reviewed. We also review a modern example of machine dynamics incorporating mechatronics, nonlinear dynamics and wave physics in magnetic launchers.

Biography:The hallmark of Moon's career has been the bridging of engineering mechanics with applied mathematics and applied physics through unique experiments. Nonlinear dynamics is a theme running through five of his books ranging from chaotic vibrations to superconducting levitation. Moon's laboratory gained world-wide recognition for its experimental work in nonlinear dynamics and chaos theory and culminated in two widely referenced books in chaos theory and experiment, one of which has been translated into Russian. [Chaotic Vibrations, 1987, 2004, Chaotic and Fractal Dynamics, 1992].

Another highly referenced area of research is magneto-mechanical dynamics especially related to fusion energy and superconducting levitation. Moon holds several patents in superconducting bearings. Some of this research may be found in Moon's books Magneto-solid Mechanics (1984), Superconducting Levitation, 1994. His lab also worked on smart structures and elastic-linked robots. Nearly two-dozen Ph.D students and many international visitors and researchers came through Moon's laboratory at Cornell in the 25 years.

These activities have resulted in over 100 invited lectures in the past twenty years all over the world, including keynote and plenary addresses at scientific meetings in Germany (1994) Israel (1996), Brazil (1997), Canada (2005). In 1988 Francis Moon was chosen as a senior Humboldt Preistrager from Germany for his work on chaotic dynamics. He was also invited to conduct short courses on chaos theory at the International Center for Mechanical Sciences (CISM) in Udine Italy. Short courses were also given at Argonne National Laboratory, NASA Langley, United Technologies Corp., University of Hannover, Germany (1995), The Brazil Association of Mechanical Engineers (1997), Technical University Vienna (1998). In 1996 Moon was elected to the National Academy of Engineering.

Early in his Cornell career he assumed the Head of the Department of Theoretical of Applied Mechanics (1980-1987) and later became the Director of the Sibley School of Mechanical and Aerospace Engineering at Cornell (1987-1992).

He was also the President of the Society of Engineering Science as well as the American Academy of Mechanics (AAM, 2000). He is a Fellow of ASME as well as AAM.

Currently Moon is engaged in research on elastic waves and instabilities in electromagnetic launchers. In recent years his research has focused on spatio-temporal complexity in nonlinear mechanical systems, including fluid structure array dynamics and clock dynamics. Francis Moon is also curator of the famous Cornell Reuleaux Collection of 19th century kinematic models. His latest book The Machines of Leonardo da Vinci and Franz Reuleaux (Springer 2007) is based on his studies of this collection. Moon is currently completing the 2nd edition of his textbook Applied Dynamics (Wiley, 2008)

Moon was recently awarded the ASME Lyapanov Award for lifetime achievement in nonlinear dynamics.

Abstract: A popular approach for reducing fuel consumption in automotive engines is to deactivate some cylinders in low-power operating conditions. These engines, which are currently offered by GM, Honda, and Chrysler, achieve fuel savings by decreases in pumping losses that occur when fewer cylinders are firing. However, they cannot currently operate in reduced-cylinder mode at low engine speeds (not even close to idle) due to high levels of vibration encountered in this operating range. By attenuating these low-speed vibrations one can improve the overall efficiency of the engine by employing a wider envelope of reduced-cylinder operation. In the present work we demonstrate that centrifugal pendulum vibration absorbers are ideally suited for this purpose. These absorbers counteract torsional vibrations at a given engine order and operate most effectively if they are designed to venture into nonlinear response regimes. Some nonlinear effects can be designed into the absorbers to provide enhanced performance, while others are detrimental to their function. In this work we consider rotating systems fitted with sets of identical absorbers, which are described by dynamic system models with permutation symmetry. This symmetry leads to responses and instabilities that can be described using the tools of dynamical systems theory. It will be shown that undesirable dynamics can be avoided by the proper selection of absorber parameters, thus optimizing absorber effectiveness. The presentation will describe modeling, analysis, controlled experiments, automotive engine testing, and remaining challenges related to these vibration absorbers.

This work is carried out jointly with Alan Haddow and Brian Feeny at MSU and Bruce Geist at Chrysler, LLC, and is currently funded by an NSF GOALI project and by Chrysler Challenge Funds.

Biography: Steve Shaw is a Professor in the Department of Mechanical Engineering at Michigan State University. He earned an A.B. in Physics (1978) and an M.S.E. in Applied Mechanics (1979) from the University of Michigan, and a Ph.D. in Theoretical and Applied Mechanics from Cornell University (1983). He has held visiting appointments at Cornell, the University of Michigan, Caltech, the University of Minnesota, and the University of California-Santa Barbara. His interests are in dynamical systems and mechanical vibrations, including applications to nonlinear vibration absorbers, micro-electro-mechanical systems, vehicle dynamics, and structural vibrations. Steve has served in editorial positions for the Journal of Applied Mechanics, Dynamics and Stability of Systems, International Journal of Bifurcation and Chaos, Archive of Applied Mechanics, Encyclopedia of Vibration, Journal of Sound and Vibration, Communications in Nonlinear Science and Numerical Simulation, and Nonlinear Dynamics. He is the recipient of best paper awards from the SAE (Arch T. Colwell Merit Award, 1997) and the ASME (Henry Hess Award, 1986), delivered keynote lectures at the JSME Symposium on Nonlinear Dynamics (Yokohama, 2001) and the IUTAM Symposium on Nonlinear Dynamics and Chaos (Ithaca, NY, 1997), presented the inaugural Sethna Lecture for the Department of Aerospace Engineering and Mechanics at the University of Minnesota (1994), and was a Westinghouse Distinguished Lecturer in the Department of Mechanical Engineering at the University of Michigan (1990). He was elected to the rank of Fellow of ASME in 1995, and regularly serves as a consultant to automotive industries.

Abstract: Rapid deformation of the brain due to acceleration of the skull is the cause of concussion, as well as more severe traumatic brain injury (TBI). High strains and strain rates induced during milder impacts may also contribute to chronic mental deficits ("dementia pugilistica") and other neuropathologies seen in boxers and other athletes. The lack of quantitative data on brain deformation during TBI has led to widespread confusion about injury mechanisms. Experimental data are also needed to refine and validate computer simulations of brain biomechanics, which are needed to develop improved measures to prevent or reduce injury. I will discuss how magnetic resonance imaging (MRI) may be used to measure how the brain deforms during acceleration of the head. I will also show how the MRI-based visualization of low-amplitude shear waves propagating through the brain can be used to estimate material properties. These techniques can provide much-needed experimental data to refine and validate computer simulations of brain injury. Finally, quantitative measurements of brain structure and mechanical properties during brain development are presented to illuminate the underlying morphogenetic processes.

Biography: Philip Bayly received his BA from Dartmouth College in Engineering Science, his MS from Brown University, and his PhD in Mechanical Engineering from Duke University in 1993. He has been on the faculty of the Department of Mechanical, Aerospace and Structural Engineering at Washington University in St. Louis since 1994. Before pursuing his doctorate he worked as a research engineer for the Shriners Hospitals and as a design engineer for Pitney Bowes. Dr. Bayly's research interests involve dynamics and vibrations in mechanical and biomedical systems; recently he has focused on the application of MR imaging to problems in biomechanics.

Abstract: We discuss concepts and applications in the area of passive targeted energy transfer (TET) in structural and mechanical systems. By TET we denote the passive, one-way (directed and irreversible on the average) transfer of vibration or shock energy from a structure to a local, dissipative essentially nonlinear attachment (oscillator) where the energy is spatially confined and locally dissipated without ‘spreading back' to the structure; the attachment then acts, in essence, as nonlinear energy sink (NES). Due to its essential nonlinearity the local attachment introduces global changes to the dynamics of the structure to which it is attached. First, we present a theoretical study of TET by considering forced coupled oscillators with attached NESs. Due to its essential (nonlinearizable) nonlinearity, an NES is capable of engaging in transient resonance with isolated or sets of structural modes at arbitrary frequency ranges; the resulting isolated or cascades of transient resonance captures (TRCs) of the dynamics on fundamental or subharmonic resonance manifolds yield broadband passive TET from the structure to the NES (this contrasts to the classical linear absorber, whose action is narrowband). TRCs are studied both analytically – by resorting to complexification / averaging analysis and slow / fast partitions of the dynamics, and numerically – superimposing wavelet transform spectra of transient responses to frequency-energy plots of the hamiltonian dynamics. Then, the relationship between the topological structure of periodic, quasi- periodic and homoclinic orbits of the underlying hamiltonian system, and TET in the dissipative one becomes clear. Application of TET is then presented for passive suppression of aeroelastic instabilities in in-flow wings. We show that passive TET from wing modes to an attached NES results in partial or even complete suppression of aeroelastic instabilities through transient or sustained resonance captures. These nonlinear modal interactions are fully investigated by combined numerical wavelet transforms, Empirical Mode Decomposition, and Hilbert transforms, which enables us to perform multi-scale identification of the strongly nonlinear transient modal interactions, and paves the way for accurate reduced-order modeling and control of such complex nonlinear dynamical phenomena. Further applications to seismic mitigation, energy harvesting and bioengineering are discussed.

Biography: Alexander F. Vakakis is currently Professor of Dynamics at the Mechanics Division of the National Technical University of Athens. He received a Diploma Degree in Mechanical Engineering from the University of Patras (1979-84), an MSc degree in Applied Mechanics from Imperial College, London (1984-85), and a PhD degree in Applied Mechanics from the California Institute of Technology (1987-90). In the past he has been faculty in the Department of Mechanical and Industrial Engineering of the University of Illinois, Urbana – Champaign (1990-2001).

Abstract: Parametric Excitation refers to dynamics problems in which the forcing function enters into the governing differential equation as a variable coefficient. The paradigm example is given by Mathieu's equation: x'' + (d + e cos t) x = 0. This has application to many engineering systems, the simplest example of which is the vertical forcing of a pendulum. In this lecture, the basics of parametric excitation will be reviewed and a variety of new results will be presented.

Biography: Prof. Rand received his Bachelor's degree from Cooper Union (1964), and his Master's (1965) and Doctorate (1967) from Columbia University. Since 1967 he has been a professor in Cornell University's Department of Theoretical and Applied Mechanics. Dr. Rand spent sabbatical leaves in the Departments of Mechanical Engineering at UC Berkeley (1982) and UCLA (1989). He was elected a Fellow of the American Society of Mechanical Engineering in 1995. Prof. Rand received teaching awards from the Engineering College at Cornell in 1986, 1993, 1995, and 2005. He is on the editorial boards of the Journal of Vibration and Control, the International Journal of Nonlinear Mechanics, and Communications in Nonlinear Science and Numerical Simulation. He has published more than 100 research papers in the areas of nonlinear dynamics and biomathematics, as well as 3 books on computer algebra and perturbation theory. His current research work involves using perturbation methods and bifurcation theory to obtain approximate solutions to differential equations arising from nonlinear dynamics problems in engineering and biology. Prof. Rand's web site.

Previous Seminar Series

• View Fall 2005 Seminar Series
• View Spring 2006 Seminar Series
• View Fall 2006 Seminar Series
• View Spring 2007 Seminar Series
• View Fall 2007 Seminar Series