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振型叠加法是常用的动力时程分析方法之一,参与计算的振型数目是影响该方法精度的重要因素。本文揭示了确定振型参与数目的质量参与系数法、振型位移控制法的数学背景及物理含义,分析了两者存在的不足。通过推导振型截断误差估计公式,提出了更合理的确定振型数目范数形式的方法。这种方法基于严密的理论推导,适用于任意动力荷载形式。计算结果表明,振型位移控制法所确定的振型数目过大,质量参与系数法提供的振型数目偏少,而本文方法更有优势。
Mode superposition method is one of the commonly used dynamic time history analysis methods. The number of modes involved in the calculation is an important factor affecting the accuracy of the method. This paper reveals the mathematical background and physical meaning of the mass participation coefficient method and the displacement control method to determine the number of modes involved, and analyzes the shortcomings of the two methods. By deriving the modal truncation error estimation formula, a more reasonable method of determining the norm form of mode shapes is proposed. This method is based on rigorous theoretical derivation and applies to any dynamic load form. The results show that the number of mode shapes determined by modal displacement control method is too large, and the number of mode shapes provided by mass participation coefficient method is less than that of the method proposed in this paper. This method is more advantageous.