The historical bases of the Rayleigh and Ritz methods
The historical bases of the Rayleigh and Ritz methods
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DOI：
10.1016/j.jsv.2004.12.021
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发表时间：
2005-11
影响因子：
4.7
通讯作者：
A. Leissa
中科院分区：
文献类型：
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作者：
A. Leissa
瑞利的经典著作理论的声音首次出版于1877年。在它是计算连续系统（弦，杆，梁，膜，板）的自由振动的基本自然频率的许多例子，通过假设的模式形状，并设置最大值的潜在的和动能在一个运动周期中彼此相等。这种方法被称为“瑞利法”。1908年，里兹提出了他著名的方法，用于确定频率和振型，选择多个容许位移函数，并最小化涉及势能和动能的泛函。然后，他证明了它在1909年详细的完全自由方板。在1911年，瑞利写了一份文件，祝贺里兹对他的工作，但指出，他本人曾使用里兹的方法在许多地方，他的书和另一出版物。随后，出现了数百篇使用该方法的研究文章和许多书籍，一些人称之为“里兹方法”，另一些人称之为“瑞利-里兹方法”。本文探讨了方法的详细，因为里兹提出了它，并作为瑞利声称已使用it. It的结论是，虽然瑞利没有解决一些问题，其中涉及最小化的频率，这些解决方案是不是由简单，直接的方法提出的里兹和随后使用的其他人。因此，瑞利的名字不应该附加到方法。
Rayleigh's classical book Theory of Sound was first published in 1877. In it are many examples of calculating fundamental natural frequencies of free vibration of continuum systems (strings, bars, beams, membranes, plates) by assuming the mode shape, and setting the maximum values of potential and kinetic energy in a cycle of motion equal to each other. This procedure is well known as “Rayleigh's Method.” In 1908, Ritz laid out his famous method for determining frequencies and mode shapes, choosing multiple admissible displacement functions, and minimizing a functional involving both potential and kinetic energies. He then demonstrated it in detail in 1909 for the completely free square plate. In 1911, Rayleigh wrote a paper congratulating Ritz on his work, but stating that he himself had used Ritz's method in many places in his book and in another publication. Subsequently, hundreds of research articles and many books have appeared which use the method, some calling it the “Ritz method” and others the “Rayleigh–Ritz method.” The present article examines the method in detail, as Ritz presented it, and as Rayleigh claimed to have used it. It concludes that, although Rayleigh did solve a few problems which involved minimization of a frequency, these solutions were not by the straightforward, direct method presented by Ritz and used subsequently by others. Therefore, Rayleigh's name should not be attached to the method.