Quasistatic approximation (QSA). When the ratio of the incident wavelength to the interface-thickness is large, the interfaces of adhesion can be modeled as a distribution of transverse and normal springs.
General problem consisting of a layered plate immersed in an acoustic fluid, in the context of the QSA. The layered plate is infinite in the and directions and has its constituent layers joined by adhesive layers. There is an interface of adhesion between each adherent and adhesive layer. Interfaces of adhesion are represented by springs. Roman numerals are used to address each medium while arabic numerals are used to address each interface. is the total number of layers plus two half-spaces and stands for the layer or interface. The symbols , etc. represent the thicknesses of the layers. In the figure, only one of the interfaces of adhesion, the one is considered to be defective.
The modeled plate. It is composed of three layers, a copper layer with thickness, an epoxy layer with thickness acting as the adhesive layer, and an aluminum layer with of thickness. It has consequently two adhesion interfaces, labeled and .
Plane wave reflection coefficient at versus the angle of incidence. The solid line represents the reflection coefficient for the plate with original adhesion stiffness, while the dashed line represents the same for the plate with the stiffness of adhesion-interface (the in-plane or component) reduced by one-half.
Detail of Fig. 4 near 3.8°.
Detail of Fig. 4 near 13.3°.
A comparison between the exact and perturbation method solution. The partial sums for the perturbation series truncated at different terms, representing the amplitude of the total reflected pressure field, is represented by the open circles “엯.” The exact solution is represented by the solid line. The homogeneous defect’s magnitude is 17% of the original interfacial stiffness component and the angle of incidence is 3.82°.
The same as in the last figure, except the defect magnitude has increased from 17% to 17.5% of the original interfacial stiffness ( component).
A comparison between the exact and perturbation method solution. Here the angle of incidence has changed to 13.34°, and the homogeneous defect’s magnitude is 40% of the original interfacial stiffness component.
The same as in the last figure, except the defect magnitude has increased from 40% to 44% of the original interfacial stiffness ( component).
A defect representing a local “kissing bond,” where only the component of the original stiffness of adhesion is affected. It is located in interface , its maximum value is 90% of the original stiffness of adhesion and its length is about .
The acoustic incident field. It is a time-harmonic Gaussian beam with about of length and incident at the plate’s top surface at an angle of 3.82°.
Spectrum of the reflected pressure field. The wave number is nondimensionalized with respect to the wave number in the fluid.
Spectrum of the scattered pressure field. Note (a) the breadth. The spectrum is significant over a broader wave number range than that depicted in Fig. 13; (b) the peaks. These are coincident with the modes identified in the plot of the reflection coefficient, Fig. 4; (c) the “backscatter.” The amplitudes of waves traveling in the negative direction are significant. These radiate strongly at the leaky angles; and (d) the convergence. The partial sums after 30 and 50 terms are practically identical.
Mechanical properties of material constituents.
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