论文标题
能量通量和遗传性粘弹性中不均匀平面波的耗散
Energy flux and dissipation of inhomogeneous plane waves in hereditary viscoelasticity
论文作者
论文摘要
（复杂）频率$ω$的不均匀的小振幅平面波是通过显示遗传性粘弹性的线性耗散材料来传播的。能量密度，能量通量和耗散是少量的二次，即位移梯度，速度和速度梯度，每种都带有频率$ω$的谐波，因此会引起恒定的恒定术语以及频率$2Ω$的不均匀平面波。二次术语通常通过时间平均来删除，但我们将其保留在此处，因为它们的幅度与时间平均数量的频率$ω$相当。在遗传性粘弹性中得出了一种新的关系，该关系连接了具有$2Ω$的频率，能量通量和耗散术语的幅度。结果表明，复杂的组速度与术语的幅度有关，频率为$2Ω$，而不是与保守材料中均质波的衰减常数术语有关。
Inhomogeneous small-amplitude plane waves of (complex) frequency $ω$ are propagated through a linear dissipative material which displays hereditary viscoelasticity. The energy density, energy flux and dissipation are quadratic in the small quantities, namely, the displacement gradient, velocity and velocity gradient, each harmonic with frequency $ω$, and so give rise to attenuated constant terms as well as to inhomogeneous plane waves of frequency $2ω$. The quadratic terms are usually removed by time averaging but we retain them here as they are of comparable magnitude with the time-averaged quantities of frequency $ω$. A new relationship is derived in hereditary viscoelasticity that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency $2ω$. It is shown that the complex group velocity is related to the amplitudes of the terms with frequency $2ω$ rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials.
