High Quality Content by WIKIPEDIA articles! In applied mathematics and mechanical engineering, the Rayleigh–Ritz method is a widely used, classical method for the calculation of the natural vibration frequency of a structure in the second or higher order. It is a direct variational method in which the minimum of a functional defined on a normed linear space is approximated by a linear combination of elements from that space. This method will yield solutions when an analytical form for the true solution may be intractable.The method is also widely used in quantum chemistry.Typically in mechanical engineering it is used for finding the approximate real resonant frequencies of multi degree of freedom systems, such as spring mass systems or flywheels on a shaft with varying cross section. It is an extension of Rayleigh's method. It can also be used for finding buckling loads for columns.

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