By J.D. Achenbach
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Extra resources for A Theory of Elasticity with Microstructure for Directionally Reinforced Composites
27) 47 Propagation of harmonic waves in anisotropic solids where pis an effective mass density. Let us consider u i =A d. 1 exp [iw (x. Q. 28) t)] where w is the (real-valued) angular frequency and the components of the slowness vector
15). 20) ( 4. 21) These expressions represent standing waves across the cross section, and progressive waves in the direction of the layer. 24a,b) By virtue of Eqs. 15 ), and Eqs; (4. 22) and (4. 23) the displacement components can be written in terms of elementary functions. For the displacement in the x 1 -direction the motion is symmetric (antisymmetric) with regard to x 2 = 0, if u 1 contains cosines (sines). The displacement in the x 2 -direction Chapter 4 46 is symmetric (antisymmetric) if u 2 contains sines (cosines).
1. 7, The frequency spectrum shown in Fig. 1. 7 clearly reveals the different nature of the propagation of sinusoidal waves at various angles of incidence. For waves propagating normal to the layering there are frequency bands in which no waves with real-valued wavenumbers can propagate. This indicates that the laminated medium acts as a wavefilter for waves propagating normal to the layering. ym. ym. 9 8 7 6 .. J OJ I! 5 --- ::t. / 4 / / / 3 2 ' ..... ,;: 0 - 't- 100 2 =10 8 Fig. 6. Phase velocity versus the wavenumber for the lowest symmetric and antisymmetric modes in the laminated medium.
A Theory of Elasticity with Microstructure for Directionally Reinforced Composites by J.D. Achenbach