
Accession Number : AD0714997
Title : Nonlinear Periodic Waves in a Bounded Medium: A Regular Perturbation Approach.
Descriptive Note : Technical rept.,
Corporate Author : LEHIGH UNIV BETHLEHEM PA CENTER FOR THE APPLICATION OF MATHEMATICS
Personal Author(s) : Mortell,Michael P.
Report Date : OCT 1970
Pagination or Media Count : 30
Abstract : A regular perturbation scheme is given for calculating small amplitude nonlinear periodic waves in a medium of finite extent. The first term in the asymptotic expansion is an arbitrary linear standing wave. The signal carried by the waves is determined from the nonlinear terms in the governing equations by an application of the Fredholm alternative. This gives a systematic scheme for calculating the corrections to the basic flow. The first problem considered is the resonant forced motion of a polytropic gas contained in a tube with its end closed. The second problem concerns the free vibration of an anharmonic lattice, or a nonlinear dispersive string. (Author)
Descriptors : (*BOUNDARY VALUE PROBLEMS, *PERTURBATION THEORY), (*WAVE PROPAGATION, NONLINEAR DIFFERENTIAL EQUATIONS), GAS FLOW, SHOCK WAVES, PERIODIC VARIATIONS, ASYMPTOTIC SERIES, NUMERICAL INTEGRATION, VIBRATION
Subject Categories : Numerical Mathematics
Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE