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There are two classes of methods that are based on series expansions: Rayleigh‐Ritz methods and weighted residual methods. This chapter considers the Rayleigh and Rayleigh‐Ritz method and the closely related assumed modes method as well as several weighted residual methods, including the Galerkin, collocation, and least squares methods. Rayleigh's method can be used most conveniently to find the approximate fundamental natural frequency of vibration of a system without having to solve the governing differential equation of motion. The assumed modes method is closely related to the Rayleigh‐Ritz method. In fact, the discrete model obtained with the assumed modes method is identical to the one obtained with the Rayleigh‐Ritz method. The main difference between the two methods is that the Rayleigh‐Ritz method is commonly used to solve the eigenvalue problem, whereas the assumed modes method is generally used to solve the forced vibration problem.
There are two classes of methods that are based on series expansions: Rayleigh‐Ritz methods and weighted residual methods. This chapter considers the Rayleigh and Rayleigh‐Ritz method and the closely related assumed modes method as well as several weighted residual methods, including the Galerkin, collocation, and least squares methods. Rayleigh's method can be used most conveniently to find the approximate fundamental natural frequency of vibration of a system without having to solve the governing differential equation of motion. The assumed modes method is closely related to the Rayleigh‐Ritz method. In fact, the discrete model obtained with the assumed modes method is identical to the one obtained with the Rayleigh‐Ritz method. The main difference between the two methods is that the Rayleigh‐Ritz method is commonly used to solve the eigenvalue problem, whereas the assumed modes method is generally used to solve the forced vibration problem.
Approximate Analytical Methods
Rao, Singiresu S. (author)
Vibration of Continuous Systems ; 671-724
2019-03-06
54 pages
Article/Chapter (Book)
Electronic Resource
English
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