Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Nonlinear Theories of Elasticity of Plates and Shells
- 2 Nonlinear Theories of Doubly Curved Shells for Conventional and Advanced Materials
- 3 Introduction to Nonlinear Dynamics
- 4 Vibrations of Rectangular Plates
- 5 Vibrations of Empty and Fluid-Filled Circular Cylindrical Shells
- 6 Reduced-Order Models: Proper Orthogonal Decomposition and Nonlinear Normal Modes
- 7 Comparison of Different Shell Theories for Nonlinear Vibrations and Stability of Circular Cylindrical Shells
- 8 Effect of Boundary Conditions on Large-Amplitude Vibrations of Circular Cylindrical Shells
- 9 Vibrations of Circular Cylindrical Panels with Different Boundary Conditions
- 10 Nonlinear Vibrations and Stability of Doubly Curved Shallow-Shells: Isotropic and Laminated Materials
- 11 Meshless Discretizatization of Plates and Shells of Complex Shape by Using the R-Functions
- 12 Vibrations of Circular Plates and Rotating Disks
- 13 Nonlinear Stability of Circular Cylindrical Shells under Static and Dynamic Axial Loads
- 14 Nonlinear Stability and Vibration of Circular Shells Conveying Fluid
- 15 Nonlinear Supersonic Flutter of Circular Cylindrical Shells with Imperfections
- Index
- References
12 - Vibrations of Circular Plates and Rotating Disks
Published online by Cambridge University Press: 08 January 2010
Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Nonlinear Theories of Elasticity of Plates and Shells
- 2 Nonlinear Theories of Doubly Curved Shells for Conventional and Advanced Materials
- 3 Introduction to Nonlinear Dynamics
- 4 Vibrations of Rectangular Plates
- 5 Vibrations of Empty and Fluid-Filled Circular Cylindrical Shells
- 6 Reduced-Order Models: Proper Orthogonal Decomposition and Nonlinear Normal Modes
- 7 Comparison of Different Shell Theories for Nonlinear Vibrations and Stability of Circular Cylindrical Shells
- 8 Effect of Boundary Conditions on Large-Amplitude Vibrations of Circular Cylindrical Shells
- 9 Vibrations of Circular Cylindrical Panels with Different Boundary Conditions
- 10 Nonlinear Vibrations and Stability of Doubly Curved Shallow-Shells: Isotropic and Laminated Materials
- 11 Meshless Discretizatization of Plates and Shells of Complex Shape by Using the R-Functions
- 12 Vibrations of Circular Plates and Rotating Disks
- 13 Nonlinear Stability of Circular Cylindrical Shells under Static and Dynamic Axial Loads
- 14 Nonlinear Stability and Vibration of Circular Shells Conveying Fluid
- 15 Nonlinear Supersonic Flutter of Circular Cylindrical Shells with Imperfections
- Index
- References
Summary
Introduction
Rotating disks are the principal components of many engineering systems, such as hard-disk drives for computers (see Figure 12.1), optical memory disks (CD and DVD), circular saws and turbines. They can be conveniently modeled as circular and annular plates by using the nonlinear equations developed in Section 1.4 of this book. When a spinning disk is subjected to a transverse load, as in the case of a reading/writing head flying over a memory disk, the disk can experience a critical speed resonance with catastrophically large vibration amplitudes whenever the rotating speed is close to a certain multiple of a natural frequency of the disk. This explains the reason for the choice of operating disks at subcritical speeds. However, the necessity of faster data access rates in disk drives is increasing the speed of such devices; this justifies the nonlinear study developed here.
In this chapter, the linear vibrations of fixed circular and annular plates is addressed first. Then, the nonlinear vibrations of free-edge circular plates is studied by using the von Kármán equations of motion for circular plates. Finally, the problem of rotating clamped-free disks is solved.
Literature review
Linear vibrations of circular and annular plates are discussed in the book by Leissa (1969).
Tobias (1957) and Williams and Tobias (1963) were among the first to study nonlinear undamped vibrations of imperfect and perfect circular plates.
- Type
- Chapter
- Information
- Nonlinear Vibrations and Stability of Shells and Plates , pp. 311 - 324Publisher: Cambridge University PressPrint publication year: 2008
References
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