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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Three-mode coupling of symmetric and antisymmetric lamb waves in plates with finite corrugations
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Three-mode coupling of symmetric and antisymmetric lamb waves in plates with finite corrugations

机译：有限波纹板中对称和反对称兰姆波的三模耦合

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摘要

Coupled-mode equations governing the amplitudes of the higher-order symmetric Lamb modes S and S with the antisymmetric mode A in an infinite elastic plate with sinusoidal surface corrugation over a finite length are obtained via multiple-scales analysis. This phenomenon of threemode coupling is observed when the wavenumbers ks1 and k of the symmetric modes and k of the antisymmetric mode satisfy the simultaneous resonance conditions k ??? k = k and k ??? k = k, where kw is the wavenumber of the sinusoidal corrugation. Near resonance, the coupled amplitude equations are solved exactly as an initial-value problem and it is seen that the modes are transmitted through the grating without reflection. Complete conversion from the symmetric modes into the antisymmetric mode is observed at periodic intervals along the grating when the resonance conditions are exactly satisfied. The effect of detuning away from resonance also shows propagation without reflection with periodic energy exchange. In the latter case, the modes couple without complete conversion. This phenomenon of mode conversion is confirmed by the results of an experiment on an aluminum plate with a triangular grating excited with the S symmetric mode at 2.7 MHz.
机译：通过多尺度分析，获得了控制高阶对称Lamb模S和S与反对称模A的振幅在有限长度上具有正弦表面波纹的无限弹性板中的耦合模方程。当对称模的波数ks1和k以及反对称模的波数满足同时谐振条件k时，观察到这种三模耦合现象。 k = k和k ??? k = k，其中kw是正弦波纹的波数。接近共振时，耦合振幅方程正好是作为一个初值问题而求解的，并且可以看出模式是通过光栅传输的，没有反射。当精确地满足共振条件时，沿着光栅以周期性间隔观察到从对称模式到反对称模式的完全转换。远离共振的失谐效应还表明传播是无反射的，具有周期性的能量交换。在后一种情况下，模式耦合而没有完全转换。这种模式转换现象已通过在铝板上以2.7 MHz的S对称模式激发的具有三角光栅的铝板上的实验结果得到了证实。

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