PHASE VELOCITY CURVES ON NEW ARBITRARILY HIGHER ORDER PLATE THEORY

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  • 任意高次板曲げ理論における位相速度曲線群
  • ニンイ コウジ イタマゲ リロン ニ オケル イソウ ソクド キョクセングン

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Abstract

The Mindlin plate theory is extended to the arbitrarily higher order plate theory. Legendre polynomial functions are logically derived as a basis warping function of the plate in the process of successive approximation. Basis shear stress functions are given by integration of the basis warping functions in the direction of plate thickness. From these two basis functions, the warping resistance matrix and the shear resistance matrix of the plate cross section about the neutral plane are given. The motion equations of the plate are derived using the Hamilton's principle, and any number of phase velocity curves can be illustrated. The defect of failure converging at the high frequency range can be solved by introducing new elasticity moduluses, which are treated as functions of frequency. The phase velocity curves are in good agreement with that of the Rayleigh-Lamb frequency equation of the theory of elasticity.

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