By Ch Zhang
This learn document includes effects acquired by way of the authors in recent times within the study sector of dynamic fracture mechanics and wave propagation in broken solids. It bargains with a number of issues on wave propagation in elastic solids with cracks. insurance comprises wave scattering difficulties via a unmarried crack, a periodic array of collinear cracks in isotropic and transversely isotropic elastic solids, interface cracks with a periodic spacing, and randomly dispensed micro-cracks. The authors current a non-hypersingular boundary indispensable equation solution to deal with single-crack wave scattering difficulties, either in time - and frequency-domain. Numerical examples are given to teach the accuracy and potency of the tactic.
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Extra resources for On wave propagation in elastic solids with cracks
70) where nc is called the complex refractive index. It is useful to work with the real and imaginary part separately, and in this way we define: nc = n − iκ where now n is the real refractive index, and κ is called the absorption index. 73) where k represents the real wavevector, and a is called the attenuation vector. 76) The planes of constant amplitude will be determined by the condition ar = constant, and therefore they will be planes perpendicular to the attenuation vector a. On the other hand, the planes of equal phase will be defined by the condition of kr = constant, and thus the phase front will be planes perpendicular to the real wavevector k.
Nevertheless, the most common situation faced in light propagation in absorbing media is the case where the vectors k and a are parallel, and such a wave is called a homogeneous wave. 80) This expression describes a wave propagating in the direction defined by the vector k0 , with a phase velocity given by v = c/n, and whose amplitude decreases exponentially in the same direction to that propagation. One important aspect concerning light propagation in absorbing media is the intensity variation suffered by the wave as it propagates.
131) To obtain the reflection and transmission coefficients it is necessary to find a second relation between the electric field amplitudes. 51). 8 shows the reflection and transmission coefficients as a function of the incident angle in the case of air–silica interface for TE incidence, where both coefficients are real in the whole range of incident angles. As can be seen, the transmission coefficient is positive, indicating that the direction of the electric field vector of the transmitted wave is coincident to that of the incident wave.