By B. A. Auld

Quantity One starts with a scientific improvement of uncomplicated recommendations (strain, rigidity, stiffness and compliance, viscous clamping) and coordinate alterations in either tensor and matrix notation. the fundamental elastic box equations are then written in a kind analogous to Maxwell's equations. This analogy is then pursued while examining wave propagation in either isotropic and anisotropic solids. Piezoelectricity and bulk wave transducers are taken care of within the ultimate bankruptcy. Appendixes record slowness diagrams and fabric houses for numerous crystalline solids. quantity applies the cloth constructed in quantity One to a number of boundary price difficulties (reflection and refraction at airplane surfaces, composite media, waveguides, and resonators). Pursuing the electromagnetic analogue, analytic options frequent in electromagnetism (for instance, common mode emissions), are utilized to elastic difficulties. ultimate chapters deal with perturbation and variational equipment. An appendix lists homes of Rayleigh floor waves on unmarried crystal substrates.

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**Example text**

We have seen that each local oscillator is not much disturbed from its unperturbed closed orbit as far as the long-time behavior is concerned, so that in the crudest approximation one could assume X(x,t) ""Xo(rp(x,t)). This idea may readily be carried over to the wavefront problem. , the locus of the wavefront, is allowed to vary slowly with y. 9) (=x-c;p(y,t) , with rp(y,t) slowly varying iny (and possibly also in t). In a more precise picture, the y-dependence of rp generally causes some deformation of the wave profile itself, just as an oscillator, if coupled to its neighbors, can no longer stay exactly on its natural orbit.

Z)dz, - -00 00 where ! and g may be arbitrary vector functions of integrals sensible. 6) where the superscript t indicates the transpose. 7) -00 As noted above, there exists at least one eigenvalue, say AO, which vanishes identically. We assume all the other eigenvalues He in the left half of the complex A plane and at a finite distance from the imaginary axis. The assumption that the 50 4. Method of Phase Description II zero eigenvalue is isolated is justified in the present single pulse (kink) problem, but by no means valid for periodic wave trains.

II(f/J) , Z(f/J) = (gradxf/J)x=xo(tP) , II(f/J) = p(Xo(f/J» . 9) The vector Z(f/J) may be called the (phase-dependent) sensitivity (Winfree, 1967), as it measures how sensitively the oscillator responds to external perturbations. 2 shows a geometrical interaction of Z(f/J). It is represented by a vector based at the point Xo(f/J) and normal to I(f/J), its length being given by the number density of surfaces I at Xo(f/J). 8), is T-periodic in f/J. 10) This equation shows that ljI is a slow variable, so that it hardly changes during the period T.

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