Coriolis effect on the vibration of flat rotating low aspect ratio cantilever plates
01 Apr 1981-Journal of Strain Analysis for Engineering Design (SAGE Publications)-Vol. 16, Iss: 2, pp 97-106
TL;DR: In this paper, the Coriolis effect on the first bending and first torsional frequencies of flat rotating low aspect ratio cantilever plates has been investigated using finite element method.
Abstract: The Coriolis effect on the first bending and first torsional frequencies of flat rotating low aspect ratio cantilever plates has been investigated using finite element method. The cantilever plate has been modelled using plane triangular shell elements with three nodes and eighteen degrees of freedom. Three typical skew angles (0, 45, and 90 degrees) and two aspect ratios (1 and 2) are considered in the analysis. In addition to the Coriolis effect other effects, namely the geometric stiffness and the supplementary stiffness, have been considered. The mass and stiffness matrices have been derived using area coordinates. It has been found that the effect of including Coriolis effect is to lower the first two frequencies. This effect is negligible when the skew angle is 90 degrees. In the other two cases, skew of 0 and 45 degrees, there is a noticeable effect on the first torsional mode frequency when the aspect ratio is unity and on the first bending mode frequency when the aspect ratio is 2. An inc...
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TL;DR: In this article, several formulas for the numerical integration of a function over a triangular area are presented, which are of the Gaussian type and are fully symmetric with respect to the three vertices of the triangle.
Abstract: Several formulas are presented for the numerical integration of a function over a triangular area. The formulas are of the Gaussian type and are fully symmetric with respect to the three vertices of the triangle.
399 citations
TL;DR: In this article, a finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc, where the plate is assumed to make any arbitrary angle with the plane of rotation of the disc.
Abstract: A finite element technique is used to determine the natural frequencies and the mode shapes of a cantilever plate mounted on the periphery of a rotating disc. The plane of the plate is assumed to make any arbitrary angle with the plane of rotation of the disc. The distributed centrifugal force is resolved into two components—one acting in the plane of the plate and the other normal to the plate. The stresses produced in the middle surface of the plate due to the in-plane forces are first determined. The increase in the bending stiffness of the plate elements due to these in-plane stresses is obtained in a manner similar to that used in the stability analysis of plates. The component of the distributed centrifugal force normal to the plate surface is added to the inertia force.
From the results of computations carried out for various values of the aspect ratio, the speed of rotation, the disc radius and the setting angle, empirical formulae are derived giving the effect of these parameters on the natural frequencies. These empirical formulae are observed to be in agreement with the corresponding known formulae for rotating cantilever beams, when the aspect ratio is high.
98 citations
TL;DR: An efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems, is presented.
Abstract: This article presents an efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems. Important applications of the present work are envisaged in the natural frequency analysis of spinning structures discretized by the finite element technique, and in the determination of transfer functions associated with the dynamic blocks of control systems of spacecraft utilizing gas jets or reaction wheels for attitude control, as well as of spin-stabilized and dual-spin-stabilized satellites. The validity of the Sturm sequence property is first established for the related matrix formulation involving Hermitian and real symmetric, positive-definite matrices, both being usually of highly banded configuration. A numerically stable algorithm based on the Sturm sequence method is then developed which fully exploits the banded form of the associated matrices.
40 citations
40 citations
TL;DR: In this article, the effect of initial stresses due to centrifugal forces or other causes change the stiffness characteristics of a solid in a manner which can be simply formulated and incorporated in a program using isoparametric solid elements and it is shown that excellent results can be obtained for a diverse range of problems.
Abstract: Initial stresses due to centrifugal forces or other causes change the stiffness characteristics of a solid in a manner which can be simply formulated.The effect is incorporated in a programme using isoparametric solid elements and it is shown that excellent results can be obtained for a diverse range of problems. Indeed the use of ‘reduced integration’ technique allows the extreme problems of thin plates and shells to be treated by the same element.The proposed formulation is particularly useful for turbine and compressor blades where the geometry changes from thick solid section to thin plate or slab.
39 citations