The procedure is illustrated by an example: intensification and refraction of acoustic signals in partially choked converging-diverging ducts. The combination of analytical and numerical techniques also can be very useful for treating linear wave propagation in nonhomogeneous media. These points are illustrated by examples drawn from structural vibration, sloshing of liquids in containers, and nonlinear stability of boundary layers. Nayfeh: Wrote: (i) 10 books in perturbation methods and nonlinear dynamics, several of them with thousands of citations, considered as the most valuable. These limitations can be removed by combining analytical and numerical techniques. However, purely analytical techniques are limited to systems with simple boundaries and composition. For weakly nonlinear systems, perturbation techniques can be used quite effectively. In many nonlinear problems in mechanics, the responses are so complicated (jumps, period-multiplying bifurcations, chaos, saturation) that it is impractical if not impossible to determine their salient features by using a purely numerical technique.
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