Vibrations of circular arches subjected to hydrostatic follower loads – computations by the use of Green functions

Kelemen, Katalin (2000) Vibrations of circular arches subjected to hydrostatic follower loads – computations by the use of Green functions. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 1 (2). pp. 167-178. ISSN 1586-2070

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Abstract

Using the Green function matrix, self adjoint eigenvalue problems governed by degenerate systems of differential equations and homogeneous linear boundary conditions can be replaced -- like the case of scalar equations -- by an eigenvalue problem for a system of Fredholm integral equations with the Green function matrix as a kernel. We have determined the Green function matrix for simply supported and fixed circular arches provided that the arch is also subjected to a hydrostatic follower load. In the knowledge of the Green function matrix, the self adjoint eigenvalue problem giving the natural frequencies of the vibrations as a function of the follower load can be replaced by an eigenvalue problem described by a system of Fredholm integral equations. The latter is reduced to an algebraic eigenvalue problem and the first eigenvalues are computed by applying the QZ algorithm. The results computed show how the load affects the first natural frequencies of the arches.

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