Nonlinear Waves in Rods
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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Rods are simple structures that are often regarded as one-dimensional continua, but because of finite transverse dimensions, propagating waves are subject to dispersion, which may mask other effects. A one-dimensional continuum theory with one internal, scalar variable can be used to model a solid rod with longitudinal waves. In this paper the material is assumed to be homogeneous, isotropic, and hyperelastic. First, the linear theory is reviewed to exhibit clearly the multiple wave hierarchy that exists in a rod. Next, expansion and scaling techniques are used in the fully nonlinear case to examine the main pulse. Finally, steady nonlinear waves are examined and both solitary waves and periodic waves are found to exist. Results are compared to the simple wave solutions available from the most elementary one-dimensional nonlinear theory for rods.
- Numerical Mathematics