Research
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Dynamics and Vibrations
Researchers at the U-M focus on dynamics and vibrations as an integral part of understanding many physical systems and technologies, ranging from MEMS sensors and devices to air and space structures to the development of novel materials. One of the key common elements of all these is the crucial time dependence of the processes governing these systems. For example, the complex dynamics of DNA supercoiling can only be described by accurate dynamic modes which take onto account their dynamic behavior, the identification of mistuning and vibration localization in turbomachinery can only be accomplished through advanced computational dynamics techniques combined with physical measurements, the understanding of the causes for the high sensitivity and resolution of sound detection in the human ear can only be discovered through novel complex and high-fidelity dynamic models.
Furthermore, U-M researchers develop novel solutions for a broad range of inverse problems in dynamics (e.g. system identification, sensing and damage detection, acoustic signal processing) which are used in technologies spanning turbomachinery, bio-engineering, naval communications and sonar detection, microphones and MEMS devices. These novel solutions depend on dynamic models and the exploitation of dynamic phenomena. Both applied and fundamental problems in linear and nonlinear dynamics are tackled. -
Research Highlights
Cellular biomechanics: collective dynamics of motor Proteins
Motor proteins are enzymes that convert chemical energy into mechanical work in the cell. They perform a multitude of vital roles including motility, cell division, long-range transport, ATP production and sensing, and are present in all forms of life from bacteria to humans. For instance, the motor protein myosin-1 is the active element in muscle contraction. Bacterial flagella are powered by rotary motor proteins. Another type of motor protein, dynein, powers flagella and cillia in eukaryotes, such as in sperm. The motor protein prestin is thought to provide the feedback mechanism that increases frequency differentiation and sensitivity in hearing. During mitosis, motor proteins are implicated in the positioning of chromosomes during metaphase. Another motor protein then cleaves the two halves apart in anaphase. The ubiquity of motor proteins in biology makes understanding their mechanisms of utmost importance.We are currently focused on kinesin-1, which is a processive molecular motor that converts the energy from ATP hydrolysis and Brownian motion into directed movement. Single-molecule techniques allow the experimental characterization of kinesin in vitro at a range of loads and ATP concentrations. Mounting evidence suggests that in the cell, several kinesin motors work collectively to transport a cargo. We develop models capable of describing the collective behavior of several coupled motors.
Sensors based on nonlinear dynamics and active interrogation
Several current micro-sensing technologies are based on vibratory responses, such as bio-chemical detectors (which use mass measurements) and tapping-mode atomic force microscopy. In those technologies, highly nonlinear systems can provide increased sensitivity and selectivity. In that context, we are creating a comprehensive and radically novel sensing paradigm which provides ultra high sensitivity, robustness, as well as multi-functional sensing capabilities (e.g. sensor self-calibration).We develop the next generation of high-sensitivity micro-fluid-structural sensors and enable fundamentally novel sensing capabilities for bio-detection, the measurement of micro-mechanical properties, the identification and characterization of micro-fluid-structural phenomena, and homeland defense applications. These capabilities are obtained by three key advancements of sensing technology: active (feedback) and nonlinear sensor interrogation; attractor-based and bifurcation-based sensing (through the identification of attractor and bifurcation morphing modes and sensitivity vector fields); and high-sensitivity sensing obtained by adaptively enhanced nonlinear dynamics.
MEMS inertial sensor applications and sports training devices
Miniature and wireless MEMS inertial measurement systems to analyze and to teach the fine motor skills required in sports and other applications. For instance, when attached to or embedded in sports equipment, our patented designs enable detailed analysis of athletic performance. To date, developed designs for sports include those for fly fishing, golf (illustration above right), baseball, hockey, bowling, crew and curling. In addition, we are actively extending our concept to support portable gait measurement, knee injury detection and surgical training.Inverse problems and system identification: modeling and identification of mistuning in bladed disks
Bladed disks such as those found in jet engines are cyclically symmetric structures. However, slight deviations from this symmetry caused by manufacturing, wear, etc. can result in a highly non-symmetric distribution of stresses during the vibration of such systems. Such a phenomenon is also known as vibration localization and leads to extremely high stresses, causing high cycle fatigue and premature failure of the structure. These deviations, known as mistuning, can be identified using reduced-order modeling techniques along with experimental response data. With the mistuning known, more accurate models can be constructed to predict the dynamics of the system (e.g. stresses and aeroelastic responses).We develop mistuning identification technology through an integrated computational and experimental research. We create novel methodologies for solving inverse problems involving complex systems, with a focus on cyclic structures. We also develop models which account for fluid-structure interactions which affect localization and high-cycle fatigue. We investigate complex, multi-stage and aeroelastic systems, and exploit localization for damage detection to enable advanced structural health monitoring.
High-sensitivity damage detection in nonlinear systems
Current vibration-based damage detection methods have significant limitations and exhibit low performance when applied to nonlinear and high-dimensional systems. We take a radically different approach, and overcome these existing limitations through the development of robust and highly sensitive nonlinear techniques for identifying the location and level of multiple, simultaneous damages. One of the enabling key advancements is our novel approach for modeling nonlinear systems using augmented linear system models.We focus on space vehicles and structures where their complex and nonlinear dynamics is monitored for assessing structural integrity. For example, we develop monitoring technology for thermal shielding components during operations such as reentry into the earth's atmosphere. Also, we develop diagnostic technology for integrated structural health monitoring of complex systems comprised of interacting structures, flows, hydraulic systems, and electromechanical components. We develop technology which can handle nonlinearities (such as Coulomb friction and cubic stiffnesses). Also, we obtain higher sensitivities by creating novel optimal auxiliary signals for system interrogation (e.g. we design nonlinear controllers for sensitivity enhancement).
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Researchers
Acoustics, time reversed acoustic processing, vibration
Structural health monitoring, nonlinear dynamics and vibration
Structural acoustics, cochlear mechanics, electroacoustic transducers
Accurate finite element methods for dynamics, phononic material design
Topology optimization for vibration
Topology optimization for vibration characteristics, negative Poisson ration material design
Dynamics of cables, dynamics/mechanics of DNA molecules, instrumentation and modeling of sports equipment
Linear and nonlinear vibrations, wave propagation in anisotropic materials
Structural dynamics and vibrations, adaptive material-based systems, structural control and health monitoring