功能梯度材料中的Bleustein-Gulyaev波
Bleustein-Gulyaev waves in some functionally graded materials
摘要：
功能梯度材料是一种性质随空间连续变化的非均匀弹性体。因此，考虑由六边形（6 mm）压电晶体制成的特殊功能梯度材料占据的半空间（x_2>0），对于该材料，弹性刚度c44、压电常数e15、介电常数ε 11和质量密度都与相同的“不均匀性函数”f（x_2）成比例地变化。然后考虑压电声剪切水平表面波的问题，它使界面（x_2=0）不受机械牵引，并随着x_2趋于无穷大而消失（Bleustein-Gulyaev波）。结果表明，对于通常的边界条件，如金属化表面或自由表面，只要选择适当的函数f，这个问题就可以精确求解。这里导出了几个这样的函数f（x_2），例如在物理学中经常遇到的exp（$ \pm 2βx_2）（β是常数），或者是周期性的或当x_2趋于无穷大时消失的其他函数;最后一个例子展示了描述分层半空间的优点，该分层半空间在远离界面处变得渐近均匀。特别注意的是，不同的不均匀性功能的影响后的特征的Bleustein-Gulyaev波（速度，色散，衰减因子，深度剖面，机电耦合因子等）。
英文摘要：
Functionally Graded Materials are inhomogeneous elastic bodies whose properties vary continuously with space. Hence consider a half-space (x_2>0) occupied by a special Functionally Graded Material made of an hexagonal (6 mm) piezoelectric crystal for which the elastic stiffness c44, the piezoelectric constant e15, the dielectric constant epsilon11, and the mass density, all vary proportionally to the same "inhomogeneity function" f(x_2), say. Then consider the problem of a piezoacoustic shear-horizontal surface wave which leaves the interface (x_2=0) free of mechanical tractions and vanishes as x_2 goes to infinity (the Bleustein-Gulyaev wave). It turns out that for some choices of the function f, this problem can be solved exactly for the usual boundary conditions, such as metalized surface or free surface. Several such functions f(x_2) are derived here, such as exp($\pm 2βx_2) (βis a constant) which is often encountered in geophysics, or other functions which are periodic or which vanish as x_2 tends to infinity; one final example presents the advantage of describing a layered half-space which becomes asymptotically homogeneous away from the interface. Special attention is given to the influence of the different inhomogeneity functions upon the characteristics of the Bleustein-Gulyaev wave (speed, dispersion, attenuation factors, depth profiles, electromechanical coupling factor, etc.)
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