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The constrained-mode solution is capable of dealing with both of these instability mechanisms.

A normal-mode solution is applied to a set of non-dimensional coupled partial differential equations.

Indeed, this snv-mode solution is even closer to the one reported by Schuh et al.

The main difference to the cna-mode solution is that the small green subclone is here at slightly higher frequencies.

The asymptotic mode solutions are taken as initial guesses for Rayleigh Quotation iteration.

The resulting normal mode solutions are compared to those obtained by the finite element analysis for several examples of transmission containing flexible gears.

Normal-mode solutions are shown for the case of a fluid layer with two pressure-release boundaries, where the bounding surfaces are given by the ramp, the Gaussian, and the sinusoidal functions, respectively.

For completeness, the counterpart for the Mode III solution is included in an appendix.

The effect of plate thickness on the mixed mode fracture solution is also investigated.

In the first mode, (NH4 2SO4 solution is passed through an ion exchange column where ammonium is concentrated in the zeolite.

The physical relevance of each type of mode for the solution is clarified through two numerical test cases, a homogeneous medium and a circular bar waveguide example, excited by a point source.