By Don Dissanayake
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Extra info for Acoustic Waves
Example text
In another word, there is only one kind of electromagnetic wave in isotropic crystal. There are two kinds of electromagnetic waves in uniaxial crystal. There are three kinds of electromagnetic waves in biaxial crystal and three kinds of distorted electromagnetic waves in monoclinic crystal. Secondly, the elastic waves and electromagnetic waves in piezoelectric solids both for static theory and for fully dynamic theory are analyzed here based on the eigen spaces of physical presentation. The results show that the number and propagation speed of elastic or electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media.
41), there are nv equations in the local phase relation of each layer. 2 Global phase relation of the structure Grouping together the local phase relations for all layers from up to down yields the global phase relation with nv × N equations a = Pd = PUd (42) where the (nv × N ) × (nv × N ) block diagonal matrices P , named the global phase matrix, is composed of Reverberation-Ray Matrix Analysis of Acoustic Waves in Multilayered Anisotropic Structures P =< P 12 , P 21 , P 23 ," , P JI , P JK ," , P N ( N + 1) , P( N + 1) N > 37 (43) the variant of the global departing wave vector d is related to the wave vector d by the (nv × N ) × (nv × N ) block diagonal matrix U , which is referred to as the global permutation matrix, to account for the different sequence of components arrangement between d and d .
25) can be further written in a form of local scattering relations on the top and bottom surfaces A 1a 1 + D1d 1 = s10 , A N + 1a N + 1 + D N + 1d N + 1 = s(0N + 1) (30) where a 1 = a 12 ( a N + 1 = a( N + 1)N ) and d 1 = d 12 ( d N + 1 = d ( N + 1) N ) are the arriving and departing wave vectors of the top (bottom) surface, A 1 = A 12 ( A N + 1 = A( N + 1)N ) and D1 = D12 ( D N + 1 = D( N + 1) N ) are nv / 2 × na12 ( nv / 2 × n(aN + 1) N ) and nv / 2 × nd12 ( nv / 2 × nd( N + 1) N ) coefficient matrices corresponding to the arriving and departing wave vectors of the top (bottom) surface, respectively.