Abstract
When we try to solve the fundamental partial differential equations on the bending vibration of a tower, it is very convenient to resort to the finite-difference equations as one of the approximate method, based on the assumption that the dimensions and the corresponding values of the sections vary continuously along its height and that they satisfy the so-called Lagrangian inter polation. As occasion demands, we have used unequidistant differences for the purpose of dividing minutely in some regions of the tower or analyzing the seismic response on a arbitrary height. In order to review the adequacy of this analysis and the accuracy of this numerical calculation, we have compared this method with the exact solution on the natural frequency and vibratory mode of homogeneous bars of the same section fixed on a rigid base. And then, we applied this method to the preliminary design of a reinforced concrete tower of multi-usuage and tried to obtain the natural frequency and vibratory mode and carry out the calculation of the seismic analysis. In view of the results so far achieved, this method was found effective in the analysis of tower-shaped structures at large, and can be well applied in various engineering problems involved in partial differential equations.
