Modal characteristics of in-plane vibration of circular plates clamped at the outer edge

We apply Hamilton's principle and model the coupled in-plane and transverse vibrations of high-speed spinning disks, which are fiber-reinforced circumferentially. We search for eigenmodes in the linear regime using a collocation scheme, and compare the mode shapes of composite and isotropic disks. As the azimuthal wavenumber varies, the radial nodes of in-plane waves are remarkably displaced in isotropic disks while they resist such displacements in composite disks. The reverse of this phenomenon happens for transversal waves and the radial nodes move toward the outer disk edge as the azimuthal wavenumber is increased in composite disks. This result is in accordance with the predictions of Nowinski's theory, and therefore, it is independent of the magnitude of the spinning velocity and the mode frequency. Although there are notable differences between the form of governing equations derived from Hamilton's principle and Nowinski's theory, transverse eigenmodes differ a little in the two approaches. We argue that the application of orthotropic composites as the core material of the next generation of hard disk drives, together with an angular velocity controller, can enhance the data access rate.

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“…(29) of KJ08, but in our formulation, they are computed from the nonoscillatory, in-plane displacement in Eq. (17). Although the term R^û in Eq.…”

Section: Transverse Modesmentioning

confidence: 97%

“…The literature of disk dynamics contains notable works on the in-plane vibrations of stationary disks [15][16][17][18]. The analytical solutions for the linearized in-plane vibrations of spinning disks was introduced by Baddour and Zu [19] who extended their analysis to nonlinearly coupled in-plane and transverse vibrations.…”

Section: Introductionmentioning

confidence: 99%

In-Plane and Transverse Eigenmodes of High-Speed Rotating Composite Disks

Dousti

Jalali

2012

Journal of Applied Mechanics

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“…Obtained results were validated by experiments. Farag and Pan [3] analyzed the modal characteristics of in-plane vibrations of a solid disk with clamped outer edge. These studies were carried out for a limited set of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Frequency equations for the in-plane vibration of orthotropic circular annular plate

Karamooz-Ravari

Forouzan

2010

Arch Appl Mech

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Orthotropic circular annular plates have a lot of applications in engineering such as space structures and rotary machines. In this paper, frequency equations for the in-plane vibration of the orthotropic circular annular plate for general boundary conditions were derived. To obtain the frequency equation, first the equation of motion for the circular annular plate in the cylindrical coordinate is derived by using the stress-straindisplacement expressions. Helmholtz decomposition is used to uncouple the equations of motion. The wave equation is obtained by assumption a harmonic solution for the uncoupled equations. Using the separation of the variables leads to the general wave equation solution and the in-plane displacements in the r and θ directions. Finally, boundary conditions are exerted and the natural frequency is derived for general boundary conditions. The obtained results are validated by comparing with the previously reported and those from finite element analysis. List of symbols ROuter radius R 0 Inner radius ξ Dimensionless coordinates r/R η Radius ratio R 0 /R ρ Density E r , E θ Youngs moduli related to the r and θ directions, respectively ν r , ν θ Poisson ratios related to r and θ directions, respectively G Modulus of elasticity in shear bStiffness ratio E θ /E r g Dimensionless shear modulus defined in text t Time σ r , σ θ Normal stress in r and θ direction respectively τ r θ shear stress ε r , ε θ Normal strain in r and θ direction respectively γ r θ Shear strain u, v Displacements in r and θ directions, respectively ϕ, H

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“…Holland [7] presented the frequency parameters and eigenmodes for a wide range of Poisson's ratios and investigated the response due to an in-plane force. Another study evaluated the frequency parameters and associated mode shapes of in-plane vibration of solid disks clamped at the outer edge using assumed deflection modes in terms of trigonometric and Bessel functions [8]. More recently, Park [9] obtained an exact frequency equation for a solid disk clamped at the outer edge.…”

Section: Introductionmentioning

confidence: 99%

In-Plane free Vibration Analysis of an Annular Disk with Point Elastic Support

Bashmal

Bhat

Rakheja

2011

Shock and Vibration

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Abstract. In-plane free vibrations of an elastic and isotropic annular disk with elastic constraints at the inner and outer boundaries, which are applied either along the entire periphery of the disk or at a point are investigated. The boundary characteristic orthogonal polynomials are employed in the Rayleigh-Ritz method to obtain the frequency parameters and the associated mode shapes. Boundary characteristic orthogonal polynomials are generated for the free boundary conditions of the disk while artificial springs are used to account for different boundary conditions. The frequency parameters for different boundary conditions of the outer edge are evaluated and compared with those available in the published studies and computed from a finite element model. The computed mode shapes are presented for a disk clamped at the inner edge and point supported at the outer edge to illustrate the free in-plane vibration behavior of the disk. Results show that addition of point clamped support causes some of the higher modes to split into two different frequencies with different mode shapes.

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Modal characteristics of in-plane vibration of circular plates clamped at the outer edge

Cited by 37 publications

References 11 publications

In-Plane and Transverse Eigenmodes of High-Speed Rotating Composite Disks

In-Plane and Transverse Eigenmodes of High-Speed Rotating Composite Disks

Frequency equations for the in-plane vibration of orthotropic circular annular plate

In-Plane free Vibration Analysis of an Annular Disk with Point Elastic Support

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