Axisymmetric seismic response of a thick circular plate supporting many rods by modal synthesis

Abstract

AbstractDynamic response of a thick, horizontal, circular plate supporting a large number of slender rods subjected to uniform boundary motion in the vertical direction has been studied by synthesizing component modes of continuous substructures. The excitation considered corresponds to the vertical component of boundary movement produced by earthquake disturbances and the axisymmetric response problem was solved. Mindlin theory was used to formulate the component equations of the plate which is treated as the main component in a modal synthesis technique. The slender rods, which are attached vertically to the plate, are handled as branch components. Vibration modes of a classical thin plate were used as the initial displacement functions for the Mindlin plate. These functions were subsequently modified by a component mode improvement process to obtain plate modes. System modes were generated by combining the improved plate modes with component modes of rods. Numerical results for the natural frequencies and time‐history response of the coupled system are compared with those given by a three‐dimensional finite element method.