複素ばねを持つ多自由度運動方程式の解法とその応用 : 第 1 報モード分離による解法

概要

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Extending the concept of Complex Spring constant to a multi-degree of freedom system, we can write the equations of motion in generalized coordinates x_i(i=1, 2, …, n) as follows; [M]{x}+[K_R+isgnωK_I]{X}=-x_0[M]{C} where [numerical formula] The characteristics of this method is that the damping valuses of each mode are appreciated independently of frequencies corresponding to the damping capacity of the structural elements in freedom systems. We make an investigation into mathematical characteristics as follows; 1) The eigenvalues and eigenvectors occur as complex conjugate pairs according to a function sgnω, which are a linearly independent set. 2) The eigenvectors establish the orthogonality properties in the eigenvectors of sgnω=1 or sgnω=-1, but the orthogonality relationships couldn't be found in the eigenvectors between sgnω=1 and sgnω=-1. 3) In view of the above mathematical properties, the n equations of motion are reduced to n pairs of uncoupled conjugate linear differential equations, and the solution can be obtained by means of mode superposition.
社団法人日本建築学会の論文
1974-06-30