We present progress we have made in developing a structural acoustic-based methodology allowing interior fault detection and localization in plate-like structures using only processed vibration data readily available on the structure's surface. Our methods use measurements of surface displacement associated with vibration of the structure caused by externally applied forces. These forces can be created simply by a local actuator in direct contact with the structure or in some cases by an incident airborne acoustic wave. The measured normal surface displacements, uz(x, y), are then inverted locally using various mathematically optimized algorithms in order to obtain a desired material parameter, for example, the elastic modulus, whose spatial variation then serves to detect and localize the fault. This structural acoustic approach is not limited to any particular length scale requiring only that the structure be mechanically excited at frequencies for which the structural wavelength is within an order of magnitude of the fault dimension and that the dynamic surface displacements be mapped with a spatial resolution smaller than the fault size. We present the results of deploying the structural acoustic technique in the US Capitol Building to locate faults within plaster walls and ceilings bearing large expanses of precious nineteenth century frescoes, in composite airframe skins in laboratory experiments to detect and locate de-bonding of thin (~1mm) stiffeners and frames, and in micro-structures to detect and locate faults in silicon micro-oscillators and their supporting structures with resolutions approaching 1μm.
In this paper, we investigate the feasibility of both detecting and localizing inclusions in structures given a knowledge of dynamic surface displacements. Provided with such displacement information, the equations of motion are utilized to estimate local material parameters through inversion, as well as to indicate the locations of inclusions using a novel generalized force mapping technique. Using a finite element code, numerical simulations were carried out for the determination of the normal surface displacements for both steel and mortar rectangular plates subject to monochromatic point actuation. The data is generated for both homogeneous plates and inhomogeneous plates within which a small rectangular inclusion of differing material parameters is present, and three algorithms are applied to the calculated displacement data. The first two are local inversion techniques which provide a spatial map of the elastic modulus normalized by density, while the third technique utilizes the inhomogeneous form of the equations of motion to obtain an induced force distribution caused by the inclusion. It will be demonstrated that the algorithms can both detect and locate inclusions in structures even when the materail parameter difference of the inclusions and the background medium is relatively low.