Green's functions for nonhomogeneous curved beams with applications to vibration problems

Kiss, László Péter (2017) Green's functions for nonhomogeneous curved beams with applications to vibration problems. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 12 (1). pp. 19-41. ISSN 1586-2070

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Abstract

In the open literature we have found no report on the Green function matrices of curved beams except papers [1,2,3] by Szeidl et al. These works assume that the material of the beam is homogeneous and isotropic. In the present paper we assume that the beam is made of heterogeneous material in such a way that the material properties depend on the cross-sectional coordinates. Under this condition we have the following aims: (1) we would like to determine the Green function matrices in a closed form for (a) fixed-fixed, (b) pinned-pinned and (c) pinned-fixed circular beams. (2) With the knowledge of the Green function matrices we can reduce the eigenvalue problems which provide the natural frequencies of the free vibrations to eigenvalue problems governed by homogeneous Fredholm integral equations. Our goal in this respect is to solve the latter eigenvalue problems numerically and compare the results obtained with the results of finite element (FE) computations. Our numerical solutions show a good agreement with commercial FE computations.

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