Nonlinear Waves in a Rod

  • Alexander Shermenev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)


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.


Transverse Wave Longitudinal Wave Bessel Function Nonlinear Wave Helmholtz Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Alexander Shermenev
    • 1
  1. 1.Wave Research CenterRussian Academy of SciencesMoscow

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