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自振周期和振型是结构抗震设计和研究的重要参数.高层建筑结构无阻尼自由振动问题总可归结为求解式(i)的广义特征值问题[K]{x}=λ[M]{x}(1)其中,λ=ω~2,[K]、[M]为对称稀疏矩阵,[K]为正定.如对[K]作三角分解,式(1)可转化为求解对称满矩阵的标准特征值问题.由于以上转化包含了求逆过程,当[K]对于求逆性态较差时,往往带来较大误差.针对上述问题,K.K.Gupta 在文献[1]中提出了行列式查找法,其主要工作量在于二分法隔离特征值,它占用计算机时长,因而较少用于结构振动计算.我们知道,高层建筑结构在不考虑扭转振动时,通常只需计算前三个振型(三个最小特征值),且目前已有一些计算自振周期的近似计算公式,这些公式比较粗糙,但通过本文的改进,可用作迭代的初始值.这样就可省去行列式查找法中的主要工作量——隔离特征值,加快了迭代速度.
Self-oscillation cycles and mode shapes are important parameters for seismic design and research of structures. The undamped free vibration problem of high-rise building structures can always be attributed to solving the generalized eigenvalue problem of formula (i) [K]{x}=λ[M]{ x} (1) where λ = ω ~ 2, [K], [M] are symmetric sparse matrices, [K] is positive definite. If [K] is trigonometrically decomposed, Eq. (1) can be converted to solve symmetric full. The standard eigenvalue problem of matrices. Because the above transformation involves the inversion process, when [K] is bad for the inversion performance state, it often brings a large error. For the above problem, KKGupta proposed in [1]. The main task of the determinant search method is the dichotomy of isolated eigenvalues. It takes up computer time and is therefore less used for structural vibration calculations. We know that when high-rise building structures are not considered for torsional vibration, they usually only need to calculate the first three. Mode shape (three minimum eigenvalues), and there are already some approximate calculation formulas for calculating the period of natural vibration, these formulas are rough, but through the improvement of this paper, it can be used as the initial value of iteration. This can eliminate the determinant Finding the main workload in the method - isolating feature values, speeds up the iterations.