๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Application of the Ritz method to the analysis of non-linear free vibrations of beams

โœ Scribed by R. Lewandowski

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
508 KB
Volume
114
Category
Article
ISSN
0022-460X

No coin nor oath required. For personal study only.

โœฆ Synopsis

This paper presents an analytical solution for geometrically non-linear free vibrations of beams with elastically supported ends in the horizontal direction. The equation of motion is obtained by employing Hamilton's principle and assuming that horizontal inertia forces can be neglected. The Ritz method, with a continuum solution and an iterative procedu-e, are used for determining the frequencies and non-linear modes of vibrations. The orthogonality conditions for these modes are also discussed. Numerical results for various beam boundary conditions are presented and compared with available results.

๐Ÿ“œ SIMILAR VOLUMES

Application of Rayleigh-Ritz and Galerki
Application of Rayleigh-Ritz and Galerkin methods to non-linear vibration of plates
โœ C.P. Vendhan; Y.C. Das ๐Ÿ“‚ Article ๐Ÿ“… 1975 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 595 KB

The difference between the three variational equations of motion and the dynamic analogue of the yon Karman equations governing the non-linear vibration of plates is considered in the context of the Rayleigh-Ritz and Galerkin methods. The non-linear free vibrations of two types of plates with in-pla

On the homotopy analysis method for non-
On the homotopy analysis method for non-linear vibration of beams
โœ T. Pirbodaghi; M.T. Ahmadian; M. Fesanghary ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 298 KB

In this study, the homotopy analysis method (HAM) is used to investigate non-linear vibration behaviour of Euler-Bernoulli beams subjected to axial loads. Analytical expressions for geometrically non-linear vibration of beams are provided. The effect of vibration amplitude on the non-linear frequenc

The element-free -Ritz method for free v
The element-free -Ritz method for free vibration analysis of conical shell panels
โœ X. Zhao; Q. Li; K.M. Liew; T.Y. Ng ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 399 KB

In this paper, the free vibration of conical panels is analyzed by the mesh-free kp-Ritz method. Both 1-D and 2-D versions of the kp-Ritz approach are formulated for conical panels. For conical panels with two simply supported straight edges, the 1-D kp-Ritz version is used, where the kernel particl