中文摘要：

根据颤振分析的基本概念，提出了一类基于矩阵奇异值理论的颤振分析新方法。该方法的特点是，以计算颤振矩阵最小奇异值或条件数的倒数来直接搜索颤振临界点。证明了这两个指标在颤振临界点处的等价性。根据指标在颤振临界点附近取极小值的特点，编制了相应的算法，在确定颤振临界点时无需计算颤振特征根，避免了“窜支”问题，从而减少了人工干预，提高了计算自动化程度。数值算例结果表明，采用该方法计算得到的颤振临界速度和颤振频率与p-k法计算结果的精度相当，且两个指标对应的计算结果一致，验证了其等价性。

英文摘要：

A new type of flutter solution based on matrix singularity is presented as a combination of the concepts of flutter and matrix analysis theories. A unique property of this method is just using the minimum singular value or inverse condition number of the flutter matrix as singularity indicators to determine the flutter boundary. These two indicators are proven to be equivalent right at the flutter point. Associated algorithm is developed for flutter solution with these indicators simply by frequency sweeping approach without solving flutter eigenvalues, which is more efficient with improvement in automation, thus requiring less human intervention. Numerical examples show that these indicators give the same flutter results as those solved by the classical p-k method, and the equivalence of these indicators is also demonstrated.