EFFECTIVE STIFFNESS THEORY FOR LAMINATED MEDIA.
NORTHWESTERN UNIV EVANSTON ILL STRUCTURAL MECHANICS LAB
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In this report a method is proposed to derive displacement equations of motion for a laminated medium. In deriving the equations the displacements of the reinforcing layers and the matrix layers are expressed as linear expansions about the midplanes of the layers. Dynamic interaction of the layers is included through continuity relations at the interfaces. The strain and kinetic energy densities of the layers are computed, where correction coefficients are introduced to compensate for errors in the strains. By means of a smoothing operation, approximate kinetic and strain energy densities for the laminated medium are obtained, and subsequent application of Hamiltons principle yields the displacement equations of motion. For the case of plane strain the equations are worked out in detail. The features of the new theory are exhibited by studying the propagation of plane free harmonic waves in an unbounded medium. Dispersion curves are shown for transverse and longitudinal motions and comparisons are made with curves obtained by using the equations of the theory of elasticity for all layers. The restrictions of the present theory are discussed, and some attention is devoted to a method of improving the results by including quadratic terms in the displacement expansions. Author
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