连续分层层共振的渐近性
Asymptotics of the resonances for a continuously stratified layer
摘要：
研究了超声波在等厚度非均匀线弹性层中的传播。相应的声传播子的共振进行了研究。结果表明，共振的分布依赖于系数的光滑性。也就是说，如果系数在边界处具有跳跃不连续性，则共振沿着平行于复频率平面的非物理薄片上的实轴的直线渐近分布。相反，如果系数是连续的，那么它表明，共振是渐近分布沿对数曲线。两个连续共振之间的间隔被证明对关节软骨退化敏感。讨论了所得结果在关节软骨超声测试中的应用。
英文摘要：
Ultrasound wave propagation in a nonhomogeneous linearly elastic layer of constant thickness is considered. The resonances for the corresponding acoustic propagator are studied. It is shown that the distribution of the resonances depends on the smoothness of the coefficients. Namely, if the coefficients have jump discontinuities at the boundaries, then the resonances are asymptotically distributed along a straight line parallel to the real axis on the unphysical sheet of the complex frequency plane. In the contrary, if the coefficients are continuous, then it is shown that the resonances are asymptotically distributed along a logarithmic curve. The spacing between two successive resonances turns out to be sensitive to articular cartilage degeneration. The application of the obtained results to ultrasound testing of articular cartilage is discussed.
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