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Journal ArticleDOI

Vibrations of cambered helicoidal fan blades

K.P. Walker1
08 Jul 1978-Journal of Sound and Vibration (Academic Press)-Vol. 59, Iss: 1, pp 35-57
TL;DR: In this article, a conforming finite shell element suitable for the analysis of curved twisted fan blades is developed and applied to a number of fan blade models, where the element is assumed to be a doubly curved right helicoidal shell, in which the curvature is shallow with respect to the twisted base plane defining the helicoid.
About: This article is published in Journal of Sound and Vibration.The article was published on 1978-07-08. It has received 38 citations till now. The article focuses on the topics: Shell (structure) & Extended finite element method.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors presented accurate non-dimensional frequency parameters for wide ranges of aspect ratio, shallowness ratio and thickness ratio for shallow shells, based on shallow shell theory.

69 citations

Journal ArticleDOI
TL;DR: Shallow shell theory and the Ritz method are employed to determine the frequencies and mode shapes of turbomachinery blades having both camber and twist, rotating with non-zero angles of attack as discussed by the authors.
Abstract: Shallow shell theory and the Ritz method are employed to determine the frequencies and mode shapes of turbomachinery blades having both camber and twist, rotating with non-zero angles of attack. Frequencies obtained for different degrees of shallowness and thickness are compared with results available in the literature, obtained from finite element analyses of nonrotating blades. Frequencies are also determined for a rotating blade, showing the effects of changing the (1) angular velocity of rotation, (2) disk radius and (3) angle of attack, as well as the significance of the most important body force terms.

60 citations

Journal ArticleDOI
TL;DR: In this article, a comprehensive study made of the free vibrations of twisted, cantilevered plates of rectangular planform is presented, and the theoretical and experimental results for models having useful ranges of aspect ratios, thickness ratios and twist angles.

51 citations

Journal ArticleDOI
TL;DR: In this article, a comprehensive study on the modeling of vibratory response of variable thickness cantilevered shallow cylindrical shells of rectangular planform is carried out through the principle of minimum total energy, the equations of stretching and bending strain energies, kinetic energy, and associated boundary conditions of the shells are derived.
Abstract: In this paper, a comprehensive study on the modeling of vibratory response of variable thickness cantilevered shallow cylindrical shells of rectangular planform is carried out. Through the principle of minimum total energy, the equations of stretching and bending strain energies, kinetic energy, and the associated boundary conditions of the shells are derived. The present model is developed based on the Ritz formulation with the assumption of sets of mathematicall y complete admissible two-dimensional polynomials to approximate the in-plane and transverse displacement amplitude functions. A basic function is introduced in the approximate method to enforce automatic satisfaction of the kinematic boundary conditions. Sets of comprehensive reasonably accurate vibration frequencies of the shallow shells are presented for wide ranges of aspect ratio, thickness variation ratios, and shallowness ratio. These results, where possible, are verified by comparing with other established experimental and theoretical solutions. Few selected contour plots for the first known mode shapes of these cylindrical shells of variable thickness are included.

50 citations

Journal ArticleDOI
W.H. Liu1, C.-C. Huang1
TL;DR: In this paper, the finite element transfer matrix method was used to study the natural frequencies of folded plate structures, and the numerical results were compared with some existing data, and fairly good agreement was achieved.

50 citations

References
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Book
01 Jan 1971
TL;DR: In this paper, the authors describe how people search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads, and instead they cope with some infectious bugs inside their computer.
Abstract: Thank you very much for downloading the finite element method in engineering science. Maybe you have knowledge that, people have search numerous times for their favorite books like this the finite element method in engineering science, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some infectious bugs inside their computer.

3,688 citations

Journal ArticleDOI
TL;DR: In this article, a general formulation for the curved, arbitrary shape of thick shell finite elements is presented along with a simplified form for axisymmetric situations, which is suitable for thin to thick shell applications.
Abstract: A general formulation for the curved, arbitrary shape of thick shell finite elements is presented in this paper along with a simplified form for axisymmetric situations. A number of examples ranging from thin to thick shell applications are given, which include a cooling tower, water tanks, an idealized arch dam and an actual arch dam with deformable foundation. A new process using curved, thick shell finite elements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformation. A general formulation for a curved, arbitrary shape of shell is developed as well as a simplified form suitable for axisymmetric situations. Several illustrated examples ranging from thin to thick shell applications are given to assess the accuracy of solution attainable. These examples include a cooling tower, tanks, and an idealized dam for which many alternative solutions were used. The usefulness of the development in the context of arch dams, where a ‘thick shell’ situation exists, leads in practice to a fuller discussion of problems of foundation deformation, etc., so that practical application becomes possible and economical.

1,205 citations

Journal ArticleDOI

437 citations

Journal ArticleDOI
TL;DR: In this paper, a conforming shallow shell finite element of arbitrary triangular shape is developed and applied to the solution of several static problems, which incorporates 36 generalized coordinates, namely the normal displacement w and its first and second derivatives plus the tangential displacements u and v and their first derivatives at each vertex.

165 citations