Hans C. Strifors

Selective reflectivity of viscoelastically coated plates in water

A detailed study of the reflection of a plane acoustic continuous wave incident on a fluid‐loaded elastic plate is presented. The purpose of the work is to determine and describe how, and how much, the reflection selectively is reduced by covering the plate with an ideally bonded viscoelastic coating. The equations of acoustics, elastodynamics, and viscoelastodynamics govern the behavior of the external fluid, the elastic plate, and the absorbing coating, respectively. By means of a recently developed viscoelastic formulation that can account for as many relaxation time constants as is physically required to model the dynamic response of the coating, the losses in the absorber can be determined. The absorbing layer can be homogeneous or inhomogeneous, with inclusions/perforations or not. The formulation is based on a general, thermodynamically admissible form of linear, isotropic viscoelasticity. Combining it with the solution of a suitably posed boundary‐value problem for the bilaminar plate, the reflect...

Backscattering of sound pulses by elastic bodies underwater

Abstract This paper studies the scattering interaction of an incident acoustic pulse and an elastic target. The pulse emerges from a distant transducer and can have any arbitrary shape and finite duration. The target is an elastic body, here assumed to be spherical and homogeneous. The Fourier integral representation of the incident pulse is combined with the resonance-scattering representation of the scattered pressure field to yield a filter-type integral that can be viewed as filtering the form function of the scatterer through the spectral window of the incident transient pulse (ping). We analyze the backscattered pulses when the incident pulses are of three simple types. The analysis is carried out in the frequency and time domains, and results are illustrated with numerical predictions for a variety of instances of increasing complexity and interest. The nature of the backscattered echo is explained in two instances for either short or long pulses. These instances correspond to cases in which the incident pulse has a carrier frequency that either coincides with any of the natural resonances of the submerged sphere or not. The main advantage of short pulses is that they can be used to replicate the (steady state) sonar cross-section of scatterers. Ultimately, if the incident pulse were a delta function in τ, the spectrum of the backscattered pulse would exactly be the form function f ∞ (π, x) divided by r . The backscattering sonar cross-section (BSCS) would then be represented by ∥f ∞ (π, x)∥ 2 . For a narrow incident continuous wave (c.w.) pulse in τ (but not infinitely narrow as is the delta function), having a carrier frequency x 0 , the replication of the BSCS would be accurate up to about that value of x 0 . Long pulses excite single target resonances and produce echoes that are quite similar to those produced by c.w. incidences. This analysis can be analogously carried out for arbitrary pulses incident on targets of more general shapes and lossy (i.e. viscoelastic) composition.

Wave propagation in isotropic linear viscoelastic media

Assuming isothermal conditions, a suitable form of the free energy is formulated for general, isotropic linear viscoelastic media. On applying a proper form of the principle of dissipation, a strong condition of dissipation is derived, which imposes restrictions on constitutive parameters of particular materials. The field equations of boundary value problems in the time domain and the frequency domain are formulated and, in particular, the problem of scattering of an acoustic pulse with plane or spherical wave front by a viscoelastic scatterer is discussed. The relation to the corresponding elastic scattering problem for steady, harmonic waves is established, and a general scheme of solution for viscoelastic scatterers is laid down.

Simultaneous classification of underground targets and determination of burial depth and soil moisture content

Target signatures extracted by ultra-wideband ground penetrating radar (GPR) will substantially depend on the targets burial depth, and on the soil’s moisture content. Using a Method-of-Moments (MoM) code, we earlier simulated such returned echoes from two targets for several moisture contents and burial depths in a soil with known electric properties. We also showed that they could then be all translated to equivalent echoes from the target at some selected standardized depth and soil moisture with adequate accuracy. The signature template of each target is here computed using a time-frequency distribution of the returned echo when the target is buried at a selected depth in the soil with selected moisture content. For any returned echo the relative difference can be computed between the target signature and a selected template signature. Using our target translation method (TTM) that signature difference can then be used as a cost function to be minimized. This is done by adjusting the depth and moisture content, now taken to be unknown parameters, using the differential evolution method (DEM). The template that gives the smallest value of the minimized cost function for a chosen returned echo is here taken to signify the classification. As it turns out, any choice of returned waveform results in correct classification of the two targets used here. Moreover, when the proper template is used, the values of the depth and moisture parameters that give the minimum cost function are good predictions of the actual target depth and soil moisture content.

Extraction of target signature features in the combined time-frequency domain by means of impulse radar

We study the scattering interaction of electromagnetic pulses of short duration with targets of either simple or complex geometrical shape using an impulse radar system. The targets of complex shape are plastic scale models of two aircraft with metallized surface. For comparison we also use a target of simple shape, in this case a metal sphere, for which we display the various signature representations, both theoretically predicted and evaluated from measured data. The form-function in the backscattering direction is determined from measured data when the targets are illuminated at a few different aspects. We extend the signature representations of targets to the combined time-frequency domain by computing and displaying pseudo-Wigner distributions of the recorded transient responses. We demonstrate that the time-frequency signature as given by the pseudo-Wigner distribution can extract and exhibit informative features in the frequency band of the incident pulse in agreement with the general time-development of resonance features. It follows that a time-frequency signature will improve the target-recognition capability ordinarily furnished by the standard form-function or radar cross-section of the considered targets.

Influence of soil properties on time-frequency signatures of conducting and dielectric targets buried underground

The capability of ultra-wideband (UWB) radar systems for extracting and displaying signature information useful for target recognition purposes has been already demonstrated. The frequency content of the projected signals is designed to match the size and kind of prospective targets and environments. Low frequencies are required for deep penetration into the ground, and high frequencies for detailed target information. Such conflicting requirements cannot always be satisfied. The complex permittivity of a soil varies substantially with its moisture content. Dry soils have a relative permittivity close to that of most dielectric mines, with low contrast and detection difficulties as consequences. Moist soils have high complex-valued dielectric constant, which may prevent sufficient penetration of the high frequencies. Moisture content of the soil and target burial depth will alter the returned echo. Moreover, moisture content of the soil and target burial depth will distort the returned echo and hence also the target signature. In the present work we investigate the backscattered radar echoes of a metal target and a dielectric target under illumination by the waveform from an aboveground radar when they are buried at a few representative depths in Yuma soil of a few different moisture contents. These echoes are simulated by the Method- of-Moments (MoM) and then used to determine the targets signatures as generated by a signal-adaptive time-frequency distribution. These time-frequency distributions can then be used as templates for actual target classification purposes using measured data.

Reception and processing of electromagnetic pulses after propagation through dispersive and dissipative media

Ultra-wideband (UWB) ground penetrating radar (GPR) systems are useful for extracting and displaying information for target recognition purposes. The frequency content of projected signals is designed to match the size and type of prospective targets and environments. The soil medium is generally dispersive and, if moist, dissipative as well. Hence, target signatures whether in the time, frequency or joint time-frequency domains, will substantially depend on the targets burial depth, and on the soils moisture content. To be useful for target recognition purposes the signatures of a given target must be known for several typical burial depths and soil moisture contents. These signatures are then used as templates in the classification process. In an attempt at reducing the number of needed templates, we focus here on the propagation of the pulses in the dissipative soil medium. Disregarding for the moment the scattering interaction with the target, we examine the distortion of the emitted interrogating pulses as they propagate through the soil and are backscattered to the receiver. We simulated such returned target echoes earlier for several burial depths using a Method-of-Moments (MoM) code. They could then be all translated to equivalent echoes from the target at some selected standardized depth and soil moisture, and vice-versa. A sufficiently accurate signal processing method for depth conversion could be employed to reduce the number of templates required for the correct classification of subsurface targets with a GPR.

Techniques for active classification of underwater structures

Various techniques for the detailed classification of submerged shells insonified by short pulses from either an active sonar or a small explosion are discussed [Ultrasonics 33, 147–153 (1995)]. The returned shell echoes in several signal domains are examined. These included the frequency, the time, and particularly the joint time‐frequency domain. The use of Wigner‐type distributions was most informative in the latter case. Selected features in these echo‐displays which provided information about a certain specific target characteristic were identified. The achieved ‘‘in situ’’ classification is rapid, unambiguous, and accurate. Examples dealing with short pulses simultaneously scattered by one, two, or more elastic shells will be shown. Theoretical predictions and measurements show good agreement. This novel analysis in the above domains determines the size, shape, wall thickness, material composition of the shell(s), and their possible filler substance(s), as well as the number of shells involved, and ...

Ultrasonic spectroscopy techniques used by dolphins to characterize resonating submerged elastic shells.

The pulsed echoes returned by several submerged cylindrical shells insonified by the peculiar sound pulses (‘‘clicks‘‘) emitted by dolphins have been examined. These clicks and echoes were collected in a large database as is done in standard dolphin experiments [Animal Sonar: Processes and Performance, edited by P. Nachtigall and P. W. B. Moore (Plenum, New York, 1988)]. The emphasis here is on the processing and physical interpretation of the ultrasonic spectroscopic features in these dolphin‐generated echoes. These resonance features actually permit the total characterization of the shells. The spectroscopic ‘‘lines’’ (i.e., resonances with widths) in the frequency signatures, as well as other features in the associated time‐domain signatures, provide all the ingredients required to determine the size, shape, thickness, shell elastic material, and internal filler material, in all cases. The time and frequency processing of the echoes is explained in detail; it follows the pattern briefly outlined elsewh...

Active classification of submerged shells insonified by dolphin ‘‘clicks.’’

Many echoes returned by various submerged shells when they are insonified by dolphin echolocation clicks have been examined. The details of the experimental tests the database collected have been described elsewhere. The signal processing analysis of the returned signatures attempted to understand how the animal performed his amazing target classification feats. The echoes were examined in the time, the frequency, and the joint time–frequency domains, and it has precisely been shown how specific features observable in these domains are directly related to the physical characteristics of the shells. The processing capitalizes on certain basic resonance features contained in the echoes, and from them it determines the size, shape, wall thickness, and the material composition of the shell and its filler substance. In the same way that these features give us the identifying characteristics of the targets with hardly any calculation required, it is believed that they also give them to the dolphin. This may exp...