Berlin; Heidelberg: Springer, 2010. - 262 p. - ISSN:1612-1384; e-ISSN:1860-6237; ISBN 978-3-642-03125-0; e-ISBN:978-3-642-03126-7Vibrations 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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InTech, Rijeka, Croatia, 2011, 236 pages
This book covers recent advances in modern vibrations analysis, from analytical methods to applications of vibrations analysis to condition monitoring. Covered topics include stochastic finite element approaches, wave theories for distributed parameter systems, second other shear deformation theory and applications of phase space to the...
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