高階微分可能な形状関数を用いた区分分割による薄肉円環板の曲げ振動解析

抄録

This paper presents a new analytical procedure on bending vibrations of an annular plate. The procedure is composed with modal expansion with mode shape functions and a finite element analysis. The plate is divided into finite number of segments. The mode shape function is introduced with the product of power series and trigonometric function. The unknown coefficients of the mode shape function are substituted by the deflection and its higher derivatives at each mode of the segments, which enables to satisfy the continuity of slope, bending moment, torsional moment, equivalent shear force at the node of segment. Discretized equations of motion of the plate are derived with Galerkin method. Natural frequencies and mode of vibrations are calculated and are compared with the exact results. Changing the ratio of inner radius to outer radius and division ratio of segment in radial direction, natural frequencies are calculated. Good agreements are obtained between the computed results and exact results of natural frequencies. In the future, this analytical procedure is expected to be applied to nonlinear vibration analysis which is sensitive to boundary condition and the continuity of deflection and its higher derivatives at segment boundaries.