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Flexural waves on narrow plates.

Andrew N Norris1

  • 1Department of Mechanical & Aerospace Engineering, Rutgers University, 98 Brett Road, Piscataway, New Jersey 08854-8058, USA. norris@jove.rutgers.edu

The Journal of the Acoustical Society of America
|May 27, 2003
PubMed
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This study analyzes flexural wave speeds in beams and plates, revealing significant differences in predictions across various theories. The finite width of plates influences wave behavior, with distinct outcomes for different theoretical models.

Area of Science:

  • Solid Mechanics
  • Wave Propagation
  • Materials Science

Background:

  • Flexural wave speeds in beams and plates are governed by bending stiffnesses, influenced by the factor (1 - nu^2).
  • Existing theories provide different predictions, especially for plates of finite lateral width and narrow geometries.

Purpose of the Study:

  • To quantitatively analyze the transition from plate to beam behavior in finite-width plates.
  • To investigate the dependence of wave speeds on plate width using asymptotic analysis.
  • To compare predictions from different classical theories (Kirchhoff, Kirchhoff-Rayleigh, Mindlin) for orthotropic and isotropic plates.

Main Methods:

  • Quantitative analysis of finite lateral width plates.
  • Asymptotic analysis to determine width dependence.

Related Experiment Videos

  • Application of Kirchhoff, Kirchhoff-Rayleigh, and Mindlin theories (with/without rotational inertia).
  • Derivation of dispersion equations for flexural edge waves.

    • Main Results:

    • Identified a frequency-dependent Young's modulus for finite-width beams/strips, with theory-dependent correction forms.
    • Observed opposite sign corrections for Kirchhoff versus Mindlin theories.
    • Demonstrated distinct behaviors and divergent predictions among the four classical theories for narrow plates.
    • Derived new dispersion equations for flexural edge waves.

    Conclusions:

    • Different plate and beam theories yield significantly distinct predictions for flexural wave speeds.
    • The behavior of narrow plates is strongly influenced by torsional wave approximations within each theory.
    • The choice of theory critically impacts the understanding of wave propagation in plates and beams.