Structural Design for Shock Mitigation

To test large structures undergoing shock loading, it is often necessary to resort, experimentally, to scale models, or numerically, to finite element models. In both cases, it is usually not feasible to build detailed models of any complex equipment attached to the test structure. Analytical and experimental work is underway to determine the pertinent dynamics which must be modeled in order to accurately predict the shock response of the primary structure.

Faculty:
Prof. Pierre Dupont; Prof. J. Gregory McDaniel

Students:
Dimitar Gueorguiev

Publications

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Optimization of Vibration and Shock Dampers

Dampers are used in a wide variety of applications to isolate structures and equipment from vibrations and shock loading through the dissipation of energy. Passive and semi-active control laws are being developed which are optimal with respect to performance criteria appropriate to the application. For systems subject to periodic excitation, for example, passive dampers which maximize energy dissipation within a given "rattle space" are being derived and implemented. For systems subject to shock loading, dampers which are optimal with respect to a class of shock inputs are of particular interest.

Faculty:
Prof. Pierre Dupont

Students:
Prakash Kasturi (former)

Publications

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Modeling Kinematic and Dynamic Properties of Remote Environments

Techniques are being developed for the automatic modeling of manipulated objects during teleoperation. The objectives of this work are twofold. Modeling information made available in real time can reduce operator error and expedite task completion. Off line, environment models can be used in virtual training systems. This work focuses on the modeling and identification of force-related properties.

Faculty:
Prof. Pierre Dupont; Prof. Robert Howe (Harvard University)

Students:
Thomas Debus

Publications

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Friction Modeling and Compensation

The nonlinear and dynamic behavior of friction is often a significant impediment to precision motion control in systems as diverse as disk drives and machine tools. There are three goals of this research. The first is to develop physically-based friction models for control and damping applications. The second is to derive techniques for on-line identification of friction parameters. The third goal is to derive control techniques which are robust with respect to variations in frictional dynamics.

Faculty:
Prof. Pierre Dupont

Publications

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Control of Fluids

Research is concerned with modeling and control design for using vortex generator jets to regulate and control the effects of boundary-layer separation. Models of various prototype fluid-structure boundaries have been developed, and novel vortex models of both controlled and uncontrolled have been used to deepen our understanding of mechanisms by which fluid stall can be controlled in applications including pitching airfoils, rotorcraft, and axial compressors.

Faculty:
Prof. John Baillieul

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Network Control Systems

Research on networked control systems involves five interrelated topics: (i) source coding of feedback signals in control applications involving rate-limited communications channels; (ii) communications and information processing strategies for coordinated control of squadrons of mobile robots; (iii) pricing as a means to allocate bandwidth and other resources in networked control systems; (iv) scheduling and routing problems for large-scale multiclass queuingnetworks; and (v) research on ad hoc optical communications.

Faculty:
Prof. John Baillieul

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Hybrid Asymptotic-Numerical Methods in Scattering

Hybrid asymptotic-numerical methods for scattering have the potential to combine the flexibility of traditional numerical methods with the efficiency of high-frequency asymptotic methods. The approach taken here is to replace the original boundary value problem (b.v.p.) with an asymptotically equivalent boundary value problem (a.b.v.p.) which can be discretized and solved readily.

The definition of a.b.v.p. depends on a preliminary analysis using the geometrical theory of diffraction. The problem domain Omega is then divided into two (not necessarily connected) subdomains Omega_A and Omega_D, where Omega_D contains all the regions of diffraction and Omega_A contains those portions of the domain where the ray ansatz is valid. The rays in Omega_A are then used as basis functions with unknown amplitudes in a variational statement of the b.v.p., thus resulting in the a.b.v.p. The resulting variational statement over the domain Omega_D=Omega/Omega_A can be discretized and efficiently solved by classical numerical methods. Continuity of the field between Omega_A and Omega_D is enforced through this specially derived variational statement.

Faculty:
Prof. Paul Barbone

Related Projects:
Structural Design for Shock Mitigation

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Shock propagation and attenuation in bubbly liquids

We study the fluid dynamics and acoustics of bubbly liquids using a continuum approach. The continuum model depends on having an "equation of state" of the bubbly liquid: a relation giving the instantaneous pressure in terms of the density, temperature and number density of bubbles, and their material time-derivatives. Our continuum models for bubbly liquids can incorporate the effects of polydispersity, mixture compressibility, and in the nonlinear case, fully nonlinear bubble dynamics. We have used this treatment to study the problem of shock waves in bubbly liquids, obtaining a simple interpretation of the essential physical phenomena that describe the oscillatory waveforms associated with such shocks. We are currently working to extend our models to account for bubble drag and inertia, thermal dissipation in bubble oscillations, and collective oscillatory effects.

Faculty:
Prof. Paul Barbone

Related Projects:
Optimization of Vibration and Shock Dampers

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Vibration of complicated systems

We study complicated vibrational systems and attempt to provide a general theory by which complicated systems can be systematically simplified. Such simplifications ease the analytical and computational burden of modeling complicated systems.

At the discrete level, a complicated system can be described as a large number of interacting oscillators which collectively model some physical system. The original application motivating this study was in structural dynamics, though our methods apply to any physical system which is modeled as a discrete set of coupled oscillators. As a step toward simplifying the analysis, we divide the entire set of oscillators into several interacting groups of oscillators, called subsystems. In the context of structural dynamics, such a step is called "substructuring." We next remove the "slave" substructures from the computational model but exactly account for their effects on the overall system dynamics. We accomplish this task by representing the subsystem through a time domain Dirichlet-to-Neumann (DtN) map. Our focus is currently on the asymptotic limit of high spectral density ("infinitely complicated subsystem"), where we have found that enormous simplifications are possible.

Besides determining accurate approximate DtN maps, we also explore efficient numerical implementations of the exact DtN maps. This requires the study and development of numerical methods for integrating Volterra integro-differential equations in time.

Faculty:
Prof. Paul Barbone

Students:
Xianghua Xu (former)

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Asymptotic methods in medical ultrasound

The formation and interpretation of B-scans depends on two key assumptions which have by now been completely utilized: one-dimensional beam propagation and nearly constant material properties. We try to exploit the existence of the small parameters underlying these assumptions within the framework of asymptotic analysis. This will allow the development of systematic improvements over the usual assumptions.

The assumption of nearly constant material properties is that which underlies the Born scattering approximation. This approximation is nonuniform in space and time, however, and so its applicability is quite limited. We have developed a renormalized Born inversion technique, which is based upon an expansion which is uniformly valid in space and time. As such, the renormalized inversions tend to be more accurate than those based on the regular Born approximation.

We have also studied forward and inverse scattering in acoustic media with microstructure. We derived effective properties for such media. An interesting case is that in which the average properties are discontinuous. For this case, we have shown the effective medium to have delta function dependence.

Faculty:
Prof. Paul Barbone

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Boundary/Trefftz Infinite Elements

Infinite elements are used to model unbounded domains. We have introduced a novel infinite element formulation based on a simple and exact variational formulation that couples two parts of an acoustics problem in a partitioned domain by weakly enforcing continuity at the interface.

This general framework encompasses as special cases most existing formulations for finite element computation in unbounded domains. The infinite elements so defined are unique in that they have unknowns only on the artificial boundary. Further, the formulation consistently allows the use of interpolations that are "incompatible" with the inner mesh, and integrations over the unbounded domain can be entirely eliminated. Our recent progress in the area has included higher order infinite elements and spectral investigations.

Faculty:
Prof. Paul Barbone

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Fluid/Elastic Wave Propagation Modeling

Faculty:
Prof. Raymond Nagem

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Acoustic Detection and Identification of Submerged Objects in Shallow Water Environment

Faculty:
Prof. Raymond Nagem

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