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
5 - Vibrations of Empty and Fluid-Filled Circular Cylindrical Shells
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
This chapter addresses the linear (small amplitude) and nonlinear (large amplitude) vibrations of circular cylindrical shells closed around the circumference (like a tube). Circular cylindrical shells are widely applied in aeronautical and aerospace engineering, in the petrol and chemical industry, in mechanical, civil, nuclear and naval engineering and in biomechanics. In fact, circular cylindrical shells are stiff structural elements that can be easily manufactured, for example, by folding and welding a metal sheet.
The linear vibrations of simply supported shells are studied by using the Donnell and the Flügge-Lur'e-Byrne theories. Fluid-structure interaction with still fluid is investigated. Numerical and experimental results are presented and compared.
The Rayleigh-Ritz method is introduced to study different boundary conditions and complicating effects, such as added masses and elastic bed.
The nonlinear vibrations of simply supported circular cylindrical shells under radial harmonic excitations are studied by using Donnell's nonlinear shallow-shell theory and the Galerkin method. For a periodic excitation applied to the circular cylindrical shell, a standing wave, symmetrical with respect to the point of application, is expected in the case of linear vibrations. This symmetrical standing wave is the driven mode. For large-amplitude vibrations, the response of the shell near resonance is given by circumferentially traveling waves, which can be in both directions (plus or minus θ). They can be described as the movement of the nodal lines of the driven mode.
- Type
- Chapter
- Information
- Nonlinear Vibrations and Stability of Shells and Plates , pp. 141 - 192Publisher: Cambridge University PressPrint publication year: 2008
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