円筒殻の振動の一解法についてFluggeの方程式にもとづくラグランジュアン

概要

論文の詳細を見る
A study of vibrations of cylindrical shells by means of the Lagrangian-minimizing-method has been made by Professor Shin Takahashi. The Lagrangian employed in his method of analysis has been found within the scope of ”Love's first approximation” based on two types of approximations;　a) The straight fibres of a shell which are perpendicular to the middle surface before deformation remain so after deformation and do not change their length, and the normal stresses in the thickness direction of the shell may be neglected in comparison with the other stresses.　b) The ratio of thickness to radii of curvatures is negligibly small compared to unity.　Flugge has obtained stress strain relations by retaining assumption a) but without the use of assumption b).　The present paper deals with the Lagrangian corresponding to the fundamental equations called ”Flugge's equation” derived from this system of stress strain relations. First, we find the strain energy of a cylindrical shell and the Lagrangian represented in terms of dispalcements. Secondly, we get the Euler equations coinciding with the Flugge equations and the boundary conditions by means of calculus of variations. Lastly, we have the solutions of this system of equations specified by the boundary values and the Lagrangian given by introducing them into itself which yields the frequency equations being minimized with respect to unknown boundary values.
山形大学の論文
1969-03-20