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Banakh L., Kempner M. Vibrations of Mechanical Systems with Regular Structure

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Banakh L., Kempner M. Vibrations of Mechanical Systems with Regular Structure
Berlin; Heidelberg: Springer, 2010. - 262 p. - ISSN:1612-1384; e-ISSN:1860-6237; ISBN 978-3-642-03125-0; e-ISBN:978-3-642-03126-7
Vibrations in systems with a periodic structure is the subject of many ongoing research activities. This work presents the analysis of such systems with the help of the theory of representation groups by finite element methods, dynamic Compliance and dynamic rigidness methods, specially adjusted for the analysis of engineering structures.
The approach presented in this book permits a simplification and facilitates the understanding of mechanical vibrations in various structures. The book includes extended studies of even complicated machinery structures with an emphasis on flight vehicle engines.
Introduction
Mechanical Vibratory Systems with Hierarchical Structure. Simulation and Calculation Methods
Introduction
Models of Mechanical Systems with Lumped Parameters
Coefficients of Static Stiffness and Compliance
Static Stiffness Coefficients for a Beam
Reduction of Models with Lumped Parameters
Coefficients of Dynamic Stiffness and Compliance
Coefficients of Dynamic Stiffness
Coefficients of Dynamic Compliance
Dimension Reduction of Dynamic Compliance Matrix
Determining Dynamic Compliance Using Experimental Methods
Fundamentals of Finite-Element Method. Analytical Approaches
Stiffness Matrix for Beam Finite Element
Stiffness Matrix for Assembled System
Boundary Conditions and Various Ways of Subsystems Connecting
Decomposition Methods Taking into Account Weak Interactions Between Subsystems
Coefficients of Dynamic Interactions
Decomposition by Partition into Independent Substructures
Other Decomposition Methods
Coefficients of Weak Interaction and Criteria for Ill–Conditions of Matrices
Systems with Lumped Parameters
Vibrations of Regular Systems with Periodic Structure
Introduction: Some Specific Features of Mechanical Systems
Wave Approach at Vibrations of Mechanical Systems with Periodic Structure
Vibrations of Frames with Periodic Structure
Combining Finite Elements Method and Dispersion Equation
Vibrations of Grate Frames
Dynamic Properties of Laminar Systems with Sparsely Positioned Laminar Ribbing
Dispersion Equation for Ribbed Laminar Systems: Conditions for Possibility of Continualization
Vibrations of a Single-Section Lamina with Laminar Ribbing: Comparison of Discrete and Continuous Models
Finite-Element Models for Beam Systems: Comparison with Distributed Parameters Models
Dispersion Equation for FE-Model of Beam
Comparing Models with Distributed Parameters and Finite Elements Models at Different FE-Mesh
Beam Systems
Hierarchy of Mathematical Models: Superposition of Wave Motions
Vibrations of Self-Similar Structures in Mechanics
Self-Similar Structures: Basic Concepts
Vibrations in Self-Similar Mechanical Structures: Dispersion Equation
Vibrations of Systems with Geometric Symmetry. Quasi-symmetrical Systems
Introduction
Basic Information about Theory of Groups Representation
Basic Concepts and Definitions
Examples of Applying Groups Representation Theory
Applying Theory of Group Representation to Mechanical Systems: Generalized Projective Operators of Symmetry
Features of Mechanical Systems with Symmetric Structure
Generalized Projective Operators and Generalized Modes
Vibrations of Frames with Cyclic Symmetry
Stiffness and Inertia Matrices
Projective Operators for Frame: Generalized Modes
Analysis of Forced Vibrations
Effect of FE-Meshon Matrix Structure
The Square Frame: Generalized Modes
Vibroisolation of Body on Symmetrical Frame: Vibrations Interaction
Quasi-symmetrical Systems
Vibrations Interaction at Slight Asymmetry
Quasi-symmetrical Systems: Free Vibrations
Quasi-symmetrical Systems: Forced Vibrations
Hierarchy of Symmetries: Multiplication of Symmetries
Periodic Systems Consisting from Symmetrical Elements
Generalized Modes in Planetary Reduction Gear due to Its Symmetry
Dynamic Model of Planetary Reduction Gear
Generalized Normal Modes in Planetary Reduction Gear: Decomposition of Stiffness Matrix
Free Vibrations
Forced Vibrations due to Slight Error in Engagement
Vibrations Interaction at Violation of Symmetry
Systems with Distributed Parameters
Basic Equations and Numerical Methods
Elementary Cells: Connectedness
Fundamental Matrices for Systems with Regular Structure
Matrices of Dynamic Compliance and Dynamic Stiffness
Mixed Dynamic Matrix
Transition Matrix
Finite Difference Equations
Mixed Dynamic Matrix as Finite Difference Equation
Transmission Matrix
Systems with Periodic Structure
Introduction
Dynamic Compliances and Stiffness for Systems with Periodic Structure
Dynamic Compliances of Single-Connectedness System
Transition Matrix
Forced Vibrations
Vibrations of Blades Package
Collective Vibrations of Blades
Systems with Cyclic Symmetry
Natural Frequencies and Normal Modes for Systems withCyclicSymmetry
Natural Frequencies
Normal Modes
Vibrations of Blades System
Different Designs of Blades Connecting
Natural Frequencies for Blades System
Normal Modes for Blades System
Numerical and Experimental Results for Blades with Shroud
Free Ring Connection
Blades with Paired-Ring Shroud
Blades Shrouded by Shelves
Systems with Reflection Symmetry Elements
Reflection Symmetry Element and Its Dynamic Characteristics
Dynamic Stiffness and Compliance Matrices for Reflection Symmetry Element
Mixed Matrix for Reflection Symmetry Element
Finite Differences Equations
Special Types of Boundary Conditions
Non closed Systems
Closed Systems
Filtering Properties of System with Reflection Symmetry Elements
Numerical Examples
Single-Connectedness Systems
Two-Connectedness Systems
Three-Connectedness System
Systems Consisting of Skew-Symmetric (Antisymmetric) Elements
Self-Similar Structures
Introductory Part: Examples of Self-Similar Mechanical Structures
Dynamic Compliances of Self-Similar Systems
Vibrations of Self-Similar Systems: Numerical Examples
Transition Matrix
Self-Similar Systems with Similar Matrix of Dynamic Compliance
Vibrations of Self-Similar Shaft with Disks
Vibrationsof Self-Similar Drum-Type Rotor
[b]Vibrations of Rotor Systems with Periodic Structure
Rotor Systems with Periodic Structure with Disks
Rotor with Arbitrary Boundary Conditions: Natural Frequencies and Normal Modes
Vibrations of Regular Ribbed Cylindrical Shells
General Theory of Shells
Dynamic Stiffness and Transition Matrix for Closed Cylindrical Shells
Dynamic Stiffness and Transition Matrix for Cylindrical Panel
Dynamic Stiffness and Transition Matrices for Circular Ring with Symmetric Profile
Vibrations of Cylindrical Shell with Ring Ribbing under Arbitrary Boundary Conditions
Vibrations of Cylindrical Shell with Longitudinal Ribbing of Non symmetric Profile
Dynamic Stiffness and Transition Matrices for Longitudinal Stiffening Ribs
Numerical Calculation of Shell with Longitudinal Ribbing
Appendix A
Stiffness and Inertia Matrices for a Ramified System Consisting of Rigid Bodies Connected by Beam Elements
Appendix B
Stiffness Matrix for Spatial Finite Element
Appendix C
Stiffness Matrix Formation Algorithm for a Beam System in Analytical Form
Appendix D
Stiffness Matrices for a Planetary Reduction Gear Subsystems
References
Index
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