Waves in Materials

The following sections are included:

• Waves Around the World

• Analysis of Waves in Linearly Deformed Elastic Materials

  • Volume and shear elastic waves in the classical approach

  • Plane elastic harmonic waves in the classical approach

  • Cylindrical elastic waves in the classical approach

  • Volume and shear elastic waves in the nonclassical approach

  • Plane elastic harmonic waves in the nonclassical approach

• Analysis of Waves in Nonlinearly Deformed Elastic Materials

  • Basic notions of the nonlinear theory of elasticity. Strains

  • Forces and stresses

  • Balance equations

  • Nonlinear elastic isotropic materials. Elastic Potentials

• Nonlinear Wave Equations

  • Nonlinear wave equations for plane waves. Methods of solving

    • Method of successive approximations

    • Method of slowly varying amplitudes

  • Nonlinear wave equations for cylindrical waves

• Comparison of Murnaghan and Signorini Approaches

  • Comparison of some results for plane waves

  • Comparison of cylindrical and plane wave in the Murnaghan model