# Rotating Shell Dynamics

There are numerous engineering applications for high-speed rotating structures which rotate about their symmetric axes. For example, free-flight sub-munition projectiles rotate at high speeds in order to achieve an aerodynamically-stable flight. This is the first book of its kind to provide a comprehensive and systematic description of rotating shell dynamics. It not only provides the basic derivation of the dynamic governing equations for rotating shells, but documents benchmark results for free vibration, critical speed and parametric resonance. It is written in a simple and clear manner making it accessible both the expert and graduate student.

Audience
Researchers and practitioners in aeronautics, astronautics, mechanical and civil engineering

Hardbound, 284 Pages

Published: January 2005

Imprint: Elsevier

ISBN: 978-0-08-044477-2

## Contents

• Chapter 1. Introduction1.1 Rotating Shells of Revolution1.2 Historical Development of the Dynamics of Shells1.3 About This Monograph
Chapter 2. Fundamental Theory of Rotating Shells of Revolution2.1 Basic Considerations and Assumptions2.2 Shell Kinematic Strain-Displacement Relations2.3 Resultant Stress-Strain Relations in Constitutive Shell Models2.4 Governing Equations of Motion2.5 Eigenvalue Analysis of Boundary Value Problems
Chapter 3. Free Vibration of Thin Rotating Cylindrical Shells3.1 Introduction3.2 Theoretical Development: Rotating Thin Cylindrical Shell3.3 Numerical Implementation3.3.1 Galerkinâs Method (Characteristic Beam Functions)3.3.2 Convergence Characteristics and Numerical Validation3.4 Frequency Characteristics3.4.1 Influence of Coriolis and Centrifugal Effects3.4.2 Different Thin Shell Theories3.4.3 Influence of Rotating Velocity3.4.4 Influence of Length and Thickness3.4.5 Influence of Layered Configuration of Composites3.4.6 Influence of Boundary Condition3.4.7 Discussion on Modal Wave NumbersAppendix
Chapter 4. Free Vibration of Thin Rotating Conical Shells4.1 Introduction4.2 Theoretical Development: Rotating Conical Shell4.3 Numerical Implementation4.3.1 Assumed-Mode Method and Generalised Differential Quadrature4.3.2 Convergence Characteristics and Numerical Validation4.4 Frequency Characteristics4.4.1 Influence of Rotating Velocity4.4.2 Influence of Cone Angle4.4.3 Influence of Length and Thickness4.4.4 Influence of Orthotropy and Layered Configuration of Composites4.4.5 Influence of Boundary Condition4.4.6 Influence of Initial Stress4.4.7 Discussion on Wave NumberAppendices
Chapter 5. Free Vibration of Thick Rotating Cylindrical Shells5.1 Introduction5.2 Natural Frequency Analysis by Mindlin Shell Theory5.2.1 Rotating Mindlin Shell Theory - Development5.2.2 Numerical Validation and Comparison5.2.3 Frequency Characteristics5.3 Analysis of Vibrational Mode by FEM with Nonlinear Kinematics5.3.1 Classification of 3-D Modes of Thick Rotating Cylindrical Shells5.3.2 Numerical Implementation5.3.3 Influence of Rotation on Frequencies of Various 3-D Modes
Chapter 6. Critical Speed and Dynamic Stability of Thin Rotating Isotropic Cylindrical Shells6.1 Introduction6.2 Theoretical Development: Axially Loaded Rotating Shells6.3 Numerical Implementation6.3.1 Critical Speed Analysis6.3.2 Dynamic Stability Analysis6.4 Critical Speeds and Instability Regions6.4.1 Influence of Axial Loading on Critical Speeds6.4.2 Parametric Studies on Dynamic Stability
ReferencesAuthor IndexSubject Index