Abstract In this work, perturbation method and Pade approximants are used to compute the eigenvalues of linear problems. This algorithm is based on the introduction of perturbation loads in the eigenvalue problem. This modified problem is solved by using the perturbation method and the Pade approximants. The computation of the eigenvalues consists then on finding the roots of the numerator of a rational fraction. To demonstrate the efficiency of the proposed method, examples of linear vibrations of plates and shells are considered. The obtained results showed that the proposed method can deal with problems with close or multiple eigenvalues. Furthermore, the results also showed that the proposed algorithm is less sensitive to the ill-conditioning of the matrices.

中文翻译：

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渐近数值方法和特征值的 Padé 近似。在板壳线性振动中的应用。

摘要 在这项工作中，微扰法和帕德逼近被用来计算线性问题的特征值。该算法基于在特征值问题中引入扰动载荷。这个修改后的问题是通过使用扰动方法和 Pade 近似来解决的。特征值的计算包括找到有理分数的分子的根。为了证明所提出方法的效率，考虑了板和壳的线性振动的例子。得到的结果表明，所提出的方法可以处理特征值接近或多个的问题。此外，结果还表明，所提出的算法对矩阵的病态条件不太敏感。