Free Vibration of Flexible Rotating Disks

Transverse vibrations of a rotating annular disk composed of two annular disks of different materials are studied in this paper. The disk is clamped at the inner edge, while at the outer edge is free. Differential equations of small vibrations are solved exactly by series expansion using the Frobenius method. The solutions are separately presented for three cases corresponding to vibration with zero, one or two nodal diameters. The influence of angular velocity, moduli of elasticity and the volume densities of the materials of disks on vibration frequency is analyzed. Vibration frequencies are obtained for the disk composed of aluminum and steel. Influences of the inner radius and the radius of the connection on the vibration frequencies are also obtained.

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“…Application of this method to plates can be found in the work of Kaplyevatsky [19], Mignolet et al [6], Eversman, Dodson [5] etc. Since Eq.…”

Section: Solving Of Differential Equations By the Frobenius Methodsmentioning

confidence: 99%

“…Eversman and Dodson [5] used the same technique to obtain an exact series representation of the solution for a fully clamped rotating disk. Mignolet et al [6] used perturbation techniques for determining frequencies and vibration mode shapes of a rotating disk.…”

Section: Introductionmentioning

confidence: 99%

Vibration and stability of rotating annular disks composed of different materials

2014

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“…The incorporation of both the bending stiffness of the disk and the effect of rotation leads to a fourth order PDE that is difficult to solve. As a result, various researchers have applied different solution techniques to the linear analysis of the free transverse vibrations of spinning disks [7,14,11,20]. In addition to considering the transverse vibrations of a spinning disk, the problem of free planar vibrations has also been investigated using linear theory [27,18,8,12,10].…”

Section: Introductionmentioning

confidence: 99%

Time-averaged canonical perturbation of nonlinear vibrations of a spinning disk

Baddour

2006

Nonlinear Analysis: Real World Applications

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“…As a result, various researchers have 0307-904X/$ -see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2005.08.004 applied different solution techniques to the linear analysis of the free transverse vibrations of spinning disks [7][8][9][10]. In addition to considering the transverse vibrations of a spinning disk, the problem of free planar vibrations has also been investigated using linear theory [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Nonlinearly coupled in-plane and transverse vibrations of a spinning disk

Baddour

2007

Applied Mathematical Modelling

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Previous nonlinear spinning disk models neglected the in-plane inertia of the disk since this permits the use of a stress function. This paper aims to consider the effect of including the in-plane inertia of the disk on the resulting nonlinear dynamics and to construct approximate solutions that capture the new dynamics. The inclusion of the in-plane inertia results in a nonlinear coupling between the in-plane and transverse vibrations of the spinning disk. The full nonlinear partial differential equations are simplified to a simpler nonlinear two degrees of freedom model via the method of Galerkin. A canonical perturbation approach is used to derive an approximate solution to this simpler nonlinear problem. Numerical simulations are used to evaluate the effectiveness of the approximate solution. Through the use of these analytical and numerical tools, it becomes apparent that the inclusion of in-plane inertia gives rise to new phenomena such as internal resonance and the possibility of instability in the system that are not predicted if the in-plane inertia is ignored. It is also demonstrated that the canonical perturbation approach can be used to produce an effective approximate solution.

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Free Vibration of Flexible Rotating Disks

Cited by 21 publications

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Vibration and stability of rotating annular disks composed of different materials

Vibration and stability of rotating annular disks composed of different materials

Time-averaged canonical perturbation of nonlinear vibrations of a spinning disk

Nonlinearly coupled in-plane and transverse vibrations of a spinning disk

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