Mathematical Modeling of Wave Propagation in Anisotropic Media (Mathematical Solution)

  • Fares A. Chedid Helou
  • John H. Hemann


Mathematical modeling of the interaction of ultrasonic waves with anisotropic media (21 constants) is carried out. An anisotropic plate immersed in a liquid medium is acted upon by an ultrasonic incident wave of arbitrary frequency and angle of incidence. The incident acoustic harmonic plane wave originates in the upper half-space fluid. Expressions for reflection and transmission coefficients are derived and presented graphically as a function of the angle of incidence and the product of the frequency and the thickness of the plate. Also, the phase of both coefficients versus frequency are presented. All field variables can be fully specified using this mathematical modeling. This study is very general and can be easily specified to special cases of wave propagation and geometric and material configurations. It can be applied to both Rayleigh and Lamb waves. The numerical computations were done through the use of the VAXIMA/MACSYMA software package.


Transmission Coefficient Anisotropic Medium Lamb Wave Orthotropic Plate Fibrous Composite 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Fares A. Chedid Helou
    • 1
  • John H. Hemann
    • 2
  1. 1.Department of Mathematical SciencesKent State UniversityAshtabulaUSA
  2. 2.Civil Engineering DepartmentCleveland State UniversityClevelandUSA

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