Nonlinear Waves in a Rod
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Computer algebra system is applied for studying the elastic torsional nonlinear waves in a rod using the second order approximation. It is shown that the nonlinear correction to the classic linear solution is a combination of a stationary longitudinal wave, a progressive longitudinal wave, and a progressive transverse wave. The solution describing a stationary longitudinal wave is a quadratic polynomial of cylindrical functions. The expressions for a progressive longitudinal wave and a progressive transverse wave inevitably include quadratures from polynomials of the cylindrical functions.
KeywordsTransverse Wave Longitudinal Wave Bessel Function Nonlinear Wave Helmholtz Equation
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