Shin Takahashi

Axisymmetric vibrations of thick shells of revolution having meridionally varying curvature.

An exact method using power series expansions is presented for solving axisymmetric free vibration problems for thick shells of revolution having meridionally varying curvature. Based on the improved thick shell theory, the Lagrangian of the shells of revolution are obtained, and the equations of motion and the boundary conditions are derived from the stationary condition of the Lagrangian. The method is applied to thick shells of revolution having their generating curves of ellipse, cycloid, parabola, catenary and hyperbola. The results by the present method are compared with those by the thin shell theory and the effects of rotatory inertia and shear deformation upon the natural frequencies and the mode shapes are clarified.

Vibrations or a Connecting System of Curved Bar : Out-of-plane

In this paper, we express the Lagrangian of out-of-plane vibrations of a uniform curved bar of which the center line is a plane curve by unknown boundary values, that is, displacements and slopes at boundary. And by using the Lagrangian, we show a method for analyzing rigorously out-of-plane vibrations of a system connecting uniform curved bars. As examples, we analyze the vibrations of a symmetric U-bar with built-in ends composed of an elliptic arc bar and straight bars and those of a catenary curved bar and straight bars and we obtain the natural frequencies and the mode shapes.

Free lateral Vibrations of rectangular sectional Bars with many circular Holes (Continued)

Free lateral vibrations of rectangular-section bars with many circular holes are studied, in which the vibrations are produced to the direction perpendicular to the axes of holes. The boundary conditions considered are as follows : one end built in and the other free, built in ends, free ends, hinged ends and one end built in and the other hinged. The method used is to determine the coefficients of normal functions according to Ritz, and it is possible to obtain the frequencies of any mode. Numerical calculations are carried out for the bars with one end built in and the other free with respect to the first and second modes and a part of the calculated results is compared with experiments.