Shane Fazzio R
Avago Technologies, Fort Collins, CO 80525, USA.
Ultrasonics. 2006 Dec;45(1-4):196-207. doi: 10.1016/j.ultras.2006.09.005. Epub 2006 Oct 16.
This paper provides a derivation of the Christoffel eigenvalue equation for acoustic wave propagation in an acoustically damped piezoelectric medium. The damping tensor is shown to couple into both the stress and displacement constitutive equations. Application of the quasi-static approximation leads to an additional term in the Christoffel equation that generates a complex k-vector, due both to introduction of a complex term and to breaking of symmetry in the left-hand side of the eigenvalue equation, subsequently resulting in damping and a phase shift for a plane wave solution. Shown are the effects of damping on the eigenvalues of the piezoelectrically stiffened Christoffel equation for plane wave propagation in unconstrained quartz over a 1 MHz to 1 GHz frequency range.
本文推导了声波在声学阻尼压电介质中传播的克里斯托费尔本征值方程。结果表明，阻尼张量耦合到应力和位移本构方程中。准静态近似的应用导致克里斯托费尔方程中出现一个额外项，该项产生一个复波矢k，这是由于引入了一个复项以及本征值方程左侧对称性的破坏，进而导致平面波解出现阻尼和相移。展示了在1MHz至1GHz频率范围内，阻尼对无约束石英中平面波传播的压电增强克里斯托费尔方程本征值的影响。
