Nedospasov I A, Mozhaev V G, Kuznetsova I E
Kotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Mokhovaya 11-7, Moscow 125009, Russia.
Physics Faculty, Lomonosov Moscow State University, Leninskie Gory 1-2, Moscow 119991, Russia.
Ultrasonics. 2017 May;77:95-99. doi: 10.1016/j.ultras.2017.01.025. Epub 2017 Feb 1.
It is found that leaky backward Lamb waves, i.e. waves with negative energy-flux velocity, propagating in a plate submerged in a liquid possess extraordinary energy properties distinguishing them from any other type of waves in isotropic media. Namely, the total time-averaged energy flux along the waveguide axis is equal to zero for these waves due to opposite directions of the longitudinal energy fluxes in the adjacent media. This property gives rise to the fundamental question of how to define and calculate correctly the energy velocity in such an unusual case. The procedure of calculation based on incomplete integration of the energy flux density over the plate thickness alone is applied. The derivative of the angular frequency with respect to the wave vector, usually referred to as the group velocity, happens to be close to the energy velocity defined by this mean in that part of the frequency range where the backward mode exists in the free plate. The existence region of the backward mode is formally increased for the submerged plate in comparison to the free plate as a result of the liquid-induced hybridization of propagating and nonpropagating (evanescent) Lamb modes. It is shown that the Rayleigh's principle (i.e. equipartition of total time-averaged kinetic and potential energies for time-harmonic acoustic fields) is violated due to the leakage of Lamb waves, in spite of considering nondissipative media.
研究发现，在浸没于液体中的平板中传播的泄漏型反向兰姆波，即具有负能量通量速度的波，具有非凡的能量特性，使其有别于各向同性介质中的任何其他类型的波。具体而言，对于这些波，由于相邻介质中纵向能量通量方向相反，沿波导轴的总时间平均能量通量等于零。这一特性引发了一个基本问题，即在这种不寻常的情况下如何正确定义和计算能量速度。应用了仅基于在板厚上对能量通量密度进行不完全积分的计算过程。角频率相对于波矢的导数，通常称为群速度，在自由板中存在反向模式的频率范围的那一部分中，恰好接近于由此平均值定义的能量速度。由于液体引起的传播型和非传播型（消逝型）兰姆模式的杂化，与自由板相比，浸没板中反向模式的存在区域在形式上有所增加。结果表明，尽管考虑的是无耗散介质，但由于兰姆波的泄漏，瑞利原理（即时谐声场中总时间平均动能和势能的均分）被违反。
