上下地震動を受ける球形ドームの応答解析

Abstract

This paper proposes respone analysis based on analytical solution in axisymmetric stateand provides some knowledge about response behaviors to vertical earthquake on the basisof nonlinear as well as of linear shell theory. Response analysis presented here introducesthe assumption of flexural vibration, approximate solution of free vibration and the Galerkin'sprocedure in modal analysis. Modal analysis entails integrations of products of deflectionmodes with respect to spatial variable, and integrals of products of these approximate modescan be reduced to functions of closed form expression even in nonlineaf state. They areeasily amenable to numerical calculation. Solving, first, linear differential equation withrespect to time variable numerically, the response characteristics of the spherical domessubjected to a real vertical earthquake will be examined and the effect of a designparameter on the response, which describes the material property, size and shape etc, willalso be discussed. Followingly, nonlinear simultaneous differential equations with respectto time variable will be solved numerically and dynamic instability of the dome during realvertical earthquake will be examined in consideration of coexistence of a few deflectionmodes.