Plane strain-elastic wave propagation is studied for two dissimilar half spaces joined together at a plane interface by an elastic bond. The bond thickness is assumed to be small compared to the wavelength, and an appropriately simplified description of the bond behavior is introduced. Attention is focused on solutions corresponding to the propagation of interface waves along the bond. The existence of interface waves is found to be governed by a parameter involving bond stiffness and wavelength. The limiting case of an infinitely stiff bond corresponds to the interface wave problem first solved by Stoneley, and it is shown that the present analysis yields Stoneley’s frequency equation in this limit. Also, the limiting case of an infinitely soft bond is found as expected to give two Rayleigh surface waves, one in each medium. It is shown analytically that, for intermediate bond stiffnesses, there may occur zero, one, or two interface waves, depending on the properties of the bond and the media. Illustrative numerical examples are presented. It is the conclusion of this study that account must be taken of the stiffness of the bond and the wavelength of the disturbance before it is proper to speak of an interface wave existing or not existing at a bonded interface.
A Timoshenko-type theory is presented for the dynamics of a cylindrical shell whose two layers are joined by a perfect bond. An assessment of the accuracy of the theory is obtained by solving the problem of axial propagation of an infinite train of axially symmetric waves and comparing the results with those obtained from the three-dimensional elasticity theory. Frequencies of the four lowest modes are accurately predicted by the shell theory for sufficiently long wavelengths and low frequencies. Preliminary comparisons of displacement distributions indicate that the shell-theory displacements are accurate in a more restricted frequency-wavelength regime. Timoshenko shear coefficients are determined by matching simple thickness-shear cutoff frequencies rather than by matching the lower Rayleigh wave speed. This is found preferable by consideration of the shapes of the first-mode phase velocity versus wave-number curves for the two theories.
Transient stress-wave experiments on laminated composites are described, and the results are compared with theoretical predictions. The composites are laminated from alternating layers of high and low-modulus material, which cause a high degree of geometric dispersion of waves propagating in the composite. Experiments were conducted in which waves propagated parallel to the laminations. Flat plates were subjected on one face to a uniform pressure with step-function time dependence induced by a gas-dynamic shock wave. Under this loading, the central portion of the specimen initially responds as if it were laterally unbounded. The average velocity over a 3/8-in-dia area of the backface of the plate was measured with a capacitance gauge. The results are in good agreement with theoretical predictions made with a long-time asymptotic approximation called the head-of-the-pulse approximation. The theory isolates the dominant character of the response and predicts timing and amplitude of oscillations in normalized rear surface velocity within a few percent.
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