This paper explores the feasibility of detecting damage within structures such as air foils by application of eddy current based techniques and reduced order modeling. To identify the geometry of a damage, an optimization algorithm is employed which requires solving the forward problem numerous times. Therefore, the forward algorithm must be solved with extremely fast and accurate solution methods. In constructing these forward methods, we employ reduced order Proper Orthogonal Decomposition (POD) techniques. The POD technique is a method which creates an 'optimal' ordered basis in the sense that information captured in the first few basis elements is maximized. One then uses a fixed number (based on a quantitative formula for percentage energy captured) of the first few basis elements, called the reduced POD basis, in the forward algorithm. Since one uses only a small number of basis elements, one is able to create a fast forward algorithm that accurately represents the relevant information. In this paper, for illustrative purposes and proof-of-concept, we consider rectangular 'cracks' parameterized by a vector parameter q representing the length, thickness, depth, center, etc. of the damage. We attempt to recapture the parameters of a damage assuming we have access to the magnetic flux density B. Our analysis uses simulated data perturbed with normally distributed noise to represent corrupted experimental data. When recapturing the length and thickness of a damage using the component of the magnetic flux density orthogonal to the eddy current flow in the sample, the methods are shown to be efficient and robust even with data containing 10% relative noise.
We first present a summary of results obtained with a numerical code to perform particle dynamics simulations of magnetorheological (MR) fluids upon application of an external magnetic field. These simulations, for the first time, account fully for all linear (long-range) magnetic interactions and are made feasible by recent developments of the Fast Multipole Method. In addition, we present some numerical and theoretical studies for the overall magnetic response in MR fluids based on nonlinear homogenization theory. We show that these results can be effectively used to study a number of experimental findings such as effective magnetic permeabilities (from the linear through saturation regimes) and response time scales, all of which are of crucial importance in the design of MR fluids.
THUNDERTM (thin-layer composite unimorph ferroelectric driver and sensor) represents a new class of piezoceramic- based actuators capable of generating significant displacements and forces in response to input voltages. The performance capabilities of THUNDERTM actuators are due to the component materials and process used in their construction. A typical THUNDERTM actuator is composed of metallic backing materials (e.g., aluminum or stainless steel), a piezoceramic wafer, and adhesive in spray or film form. The materials are bonded under high pressures and temperatures and then cooled to room temperature after the adhesive has solidified. Due to the prestresses which result from the differing thermal properties of the component materials under cooling, the actuator is highly durable with respect to mechanical impacts and voltage levels. As a result of this construction voltages in excess of 800 V can be applied to new actuator models without causing damage. This provides the actuators with significant displacement and force capabilities. In this paper, we discuss the development of evaluation criteria which are suitable for characterizing the actuator capabilities and provide a legitimate methodology for comparing THUNDERTM properties with those of other smart material actuators. For example, the concept of blocked force is often used to quantify the force capabilities of an actuator. However due to the inherent curvature and mode of operation, standard techniques for measuring blocked forces are inappropriate for THUNDERTM actuators. Furthermore, changing operating conditions, frequency, etc., often make blocked force measurements ambiguous. We will discuss techniques for evaluating THUNDERTM properties in a manner which limits such ambiguities when comparing with other smart materials. We note that the evaluation issues discussed here are germane to a variety of high performance smart material transducers.
This paper summarizes techniques for modeling geometric properties of THUNDER actuators which arise in the fabrication process. These actuators are high performance composites comprised of layers of piezoceramics in combination with aluminum, stainless steel, brass or titanium bonded with hot- melt adhesive. During the construction process, the assembly is heated under pressure to high temperatures, cooled and repoled to restore the actuator capabilities. This process provides the actuators with the robustness necessary to withstand the high voltages required for large displacement and force outputs. The process also provides the actuators with their characteristic curved shape. In this paper, relations between the thermal and electrostatic properties of the material and the final geometric configuration are quantified. This provides an initial model that can be employed in control applications which employ THUNDER actuators.
Nondestructive damage detection is an important issue in aging civil engineering, aerospace structures, and several other areas. This study presents an attempt to use parameterized partial differential equations and Galerkin approximation techniques to detect and locate damage. Dynamical analysis is carried out using structure bonded piezoceramic patches as both sensors and actuators. Our presentation demonstrates the flexibility and accuracy of this approach. It is mode independent and can sense the presence of damage and locate certain damages to a satisfactory precision. As an example, a beam with a pair of piezoceramic patches bonded to it is used as the test structure; several computational examples with holes of different size, shape, and location in the beam are investigated.
KEYWORDS: Acoustics, Systems modeling, Feedback control, Data modeling, Control systems, Radon, Actuators, 3D modeling, Ferroelectric materials, Vibration control
A problem of continued interest concerns the control of vibrations in a flexible structure and the related problem of reducing structure-borne noise in structural acoustic systems. In both cases, piezoceramic patches bonded to the structures have been successfully used as control actuators. Through the application of a controlling voltage, the patches can be used to reduce structural vibrations which in turn leads to methods for reducing structure-borne noise. A PDE-based methodology for modeling, estimating physical parameters, and implementing a feedback control scheme for problems of this type is discussed. While the illustrating example is a circular plate, the methodology is sufficiently general so as to be applicable in a variety of structural and structural acoustic systems.
A fully coupled mathematical model describing the dynamics of a cylindrical structural acoustics problem is presented. The geometry of interest consists of an acoustic field lying inside a vibrating thin cylindrical shell. In this model, the shell dynamics are coupled to the interior acoustic field through pressure and momentum conditions. Because the model will ultimately be used in control applications involving piezoceramic actuators, the loads and material contributions resulting from bonded piezoceramic patches are also included in the discussion. Strong and weak forms of the modeling set of coupled partial differential equations (PDE's) are presented, thus yielding a framework which is amenable to the application of various approximation techniques to the problem of developing schemes for forward simulations, parameter estimation, and application of PDE-based control strategies.
In this lecture we give fundamental well-posedness results for a variational formulation of a class of damped second order partial differential equations with unbounded input or control coefficients. Included as special cases in this classare structures with piezoceramic actuators. We consider approximation techniques leading to computational methods in the context of both parameter estimation and feedback control problems for these systems. Rigorous convergence results for parameter estimates and feedback gains are discussed.
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