WAVE MOTION IN SOLIDS WITH LAMELLAR STRUCTURING.
NORTHWESTERN UNIV EVANSTON ILL STRUCTURAL MECHANICS LAB
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The dynamic behavior of an unbounded medium with lamellar structuring shows a marked dependence on the ratio of the wave length and a length characterizing the layering of the medium. In this paper the time-harmonic vibrations of a laminated medium are analyzed both by employing the equations of the theory of elasticity for each layer, and by employing an approximate continuum theory for the layered medium. The frequency equations, which indicate a notable dispersive behavior, are determined according to the exact and approximate theories. A comparison of the exact and approximate frequency-versus-wavenumber curves shows good agreement. The propagation of time-harmonic waves in a laminated plate is then studied by means of plate equations based on the continuum theory for the layered medium. The dispersion curve for flexural motion is compared with an exact curve, and it is observed that both curves show like qualitative behavior, which is characterized by increasing phase velocities as the wave number increases. By contrast, a corresponding curve based on a continuum theory which does not take into account the lamellar structuring of the plate shows a constant phase velocity beyond a certain wave number. Author