Vibration Mechanics

A Research-oriented Tutorial
1. Auflage 2022
ISBN: 978-981-16-5456-5
Verlag: Springer

Buch, Englisch, 497 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 928 g

This book is a novel tutorial for research-oriented study of vibration mechanics. The book begins with twelve open problems from six case studies of vibration mechanics in order to guide readers in studying the entire book. Then, the book surveys both theories and methods of linear vibrations in an elementary course from a new perspective of aesthetics of science so as to assist readers to upgrade their way of learning. The successive chapters offer a theoretical frame of linear vibrations and waves, covering the models of vibration systems, the vibration analysis of discrete systems, the natural vibrations of one-dimensional structures, the natural vibrations of symmetric structures, and the waves and vibrations of one-dimensional structures. The chapters help readers solve the twelve open problems step by step during the research-oriented study.
The book tries to arouse the interest of graduate students and professionals, who have learnt an elementary course of vibration mechanics of two credits, to conduct the research-oriented study and achieve a helical upgrade understanding to vibration mechanics.

Zielgruppe

Graduate

Autoren/Hrsg.

Hu, Haiyan

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
• Mathematik | Informatik EDV | Informatik Informatik Berechenbarkeitstheorie, Komplexitätstheorie

Inhaltsverzeichnis

1 Start of Research-oriented Study 11.1 Needs for Research-oriented Study 11.2 Case Studies and Associated Problems 31.2.1 Preliminary study of a tethered satellite 41.2.2 Design of a hydro-elastic vibration isolation system 81.2.3 Two kinds of immovable points in a vibration system 111.2.4 Identical natural frequencies of different structures 151.2.5 Closely distributed natural modes of a symmetric structure 181.2.6 Transient response of a slender structure 211.3 Scope and Style of the Book 231.4 Further Reading and Thinking 252 Preparation of Research-oriented Study 272.1 Briefs of Beauty of Science 272.2 Beautiful Features of Vibration Mechanics 292.2.1 Unity 292.2.2 Simplicity 312.2.3 Regularity 342.2.4 Symmetry 372.2.5 Singularity 422.3 Enlightenments of Beauty of Vibration Mechanics 472.3.1 Methods of thinking 472.3.2 Aesthetic literacy 522.4 Concluding Remarks 542.5 Further Reading and Thinking 553 Models of Vibration Systems 573.1 Continuous Systems and Their Discrete Models 583.1.1 Dynamic models of continuous systems 583.1.2 Preconditions of discretization 663.1.3 Case studies of discretization 733.1.4 Concluding remarks 803.2 A Half Degree of Freedom of Discrete Systems 813.2.1 Degeneration of a degree of freedom 813.2.2 Conventional concept of degree of freedom 833.2.3 Degree of freedom based on accessible manifolds 863.2.4 Demonstrative systems with a non-holonomic constraint 903.2.5 Demonstrative systems with two non-holonomic constraints 973.2.6 Concluding remarks 1063.3 Structural Damping 1073.3.1 Frequency-invariant damping and its limitations 1083.3.2 Frequency-variant damping model and system response 1113.3.3 An approximate viscous damping model 1143.3.4 An approximate viscoelastic damping model 1163.3.5 Concluding remarks 1233.4 Further Reading and Thinking 1244 Vibration Analysis of Discrete Systems 1274.1 Vibration Systems with Non-holonomic Constraints 1284.1.1 Dynamic analysis in time domain 1284.1.2 Dynamic analysis in frequency domain 1414.1.3 Concluding remarks 1454.2 Node Number of a Natural Mode Shape 1464.2.1 Reexamination of current results 1484.2.2 Rules of node numbers of 2-DoF systems 1534.2.3 Design feasibility of nodes in a mode shape 1594.2.4 Concluding remarks 1624.3 Anti-resonances of a Harmonically Excited System 1634.3.1 Anti-resonances of 2-DoF systems 1644.3.2 Mechanisms behind two kinds of anti-resonances 1664.3.3 Design feasibility of anti-resonances 1714.3.4 Concluding remarks 1764.4 Dynamic Modifications of a System 1774.4.1 Frequency response of a composite system 1784.4.2 Adjusting an anti-resonance of a primary system 1814.4.3 Adjusting resonances of a primary system 1844.4.4 Concluding remarks 1924.5 Further Reading and Thinking 1935 Natural Vibrations of One-dimensional Structures 1955.1 Natural Vibrations of a Tether Pendulum 1955.1.1 Dynamic equation of a tether pendulum 1965.1.2 Analysis of natural vibrations 1995.1.3 Comparison between continuous model and discrete models 2075.1.4 Concluding remarks 2095.2 Duality Analysis of Rods in Natural Vibrations 2105.2.1 A dual of different cross-sections 2125.2.2 A dual of identical cross-sections 2185.2.3 A dual of two uniform rods 2235.2.4 A dual of two rods with axially varying material properties 2255.2.5 Concluding remarks 2285.3 Duality Analysis of Beams in Natural Vibrations 2285.3.1 A dual of different cross-sections 2305.3.2 A dual of identical cross-sections 2385.3.3 A dual of two uniform beams 2475.3.4 Concluding remarks 2515.4 Further Reading and Thinking 2526 Natural Vibrations of Symmetric Structures 2556.1 Natural Vibrations of Mirror-symmetric Structures 2566.1.1 Decoupling of mirror-symmetric structures 2576.1.2 Free vibrations of thin rectangular plates 2676.1.3 Repeated natural frequencies of a thin rectangular plate 2726.1.4 Close natural frequencies of a thin rectangular plate 2826.1.5 Concluding remarks 2926.2 Vibration Computations of Cyclosymmetric Structures 2936.2.1 Decoupling a cyclosymmetric structure without a central axis 2956.2.2 Decoupling a cyclosymmetric structure with a central axis 3126.2.3 High-efficient computation based on modal reduction 3236.2.4 Concluding remarks 3316.3 Modal Properties of Cyclosymmetric Structures 3326.3.1 Modal properties in representative subspaces of cyclic group 3336.3.2 Modal properties in physical space 3366.3.3 Central displacements in mode shapes 3436.3.4 Orthogonality of mode shapes with repeated frequencies 3506.3.5 Modal test of a bladed disc model 3546.3.6 Concluding remarks 3586.4 Further Reading and Thinking 3597 Waves and Vibrations of One-dimensional Structures 3617.1 Non-dispersive Waves of Rods 3627.1.1 Wave analysis of an infinitely long rod 3627.1.2 Complex function analysis of waves of an infinitely long rod 3697.1.3 Harmonic wave analysis of a finitely long rod 3737.1.4 Harmonic vibration analysis of a finitely long rod 3807.1.5 Concluding remarks 3867.2 Dispersive Waves of Rods 3877.2.1 Dispersive waves in a rod due to non-uniform cross-section 3897.2.2 Dispersive waves of a rod due to transverse inertia 4017.2.3 Dispersive waves of a rod due to an elastic boundary 4077.2.4 Concluding remarks 4127.3 Waves in a Rod Impacting a Rigid Wall 4137.3.1 Wave analysis of an impacting uniform rod 4147.3.2 Modal analysis of an impacting uniform rod 4217.3.3 Influence of non-uniform cross-section 4297.3.4 Influence of transverse inertia 4387.3.5 Criteria of modal truncation 4437.3.6 Concluding remarks 4477.4 Free Waves and Vibrations of Beams 4487.4.1 Free waves of an Euler-Bernoulli beam 4487.4.2 Free waves of a Timoshenko beam 4557.4.3 Natural vibrations of a Timoshenko beam 4667.4.4 Concluding remarks 4747.5 Forced Waves and Vibrations of Beams 4757.5.1 Waves of an infinitely long beam to a transverse harmonic force 4757.5.2 Vibrations of a finitely long beam to a transverse harmonic force 4807.5.3 Impact response of a clamped-free beam 4847.5.4 Concluding remarks 4947. 6 Further Reading and Thinking 495Appendix Three-Dimensional Waves in an Elastic Medium 497A1 Description of Three-dimensional Waves 497A1.1 Elasto-dynamic equations of a three-dimensional medium 497A1.2 Helmholtz decomposition of a displacement field 500A1.3 Solutions of three-dimensional wave equations 505A2 Two Kinds of Simple Waves 508A2.1 Planar waves 509A2.2 Spherical waves 517A3 Wave Reflections at Boundary of a Semi-infinite Medium 519A3.1 Reflections of a P-wave and an SV-wave 520A3.2 Reflection of an SH-wave 536A3.3 Rayleigh surface waves 541Bibliography 549Subject Index 553

Über Autor(innen)

Dr. Haiyan Hu is Professor of Mechanics at Beijing Institute of Technology, where he served as President from 2007 to 2017. Prior to that appointment, he was President of Nanjing University of Aeronautics and Astronautics, China from 2001 to 2007, Professor of Mechanics at that university from 1994 to 2007, and a Humboldt Research Fellow at University of Stuttgart, Germany from 1992 to 1994.Prof. Hu has made recognized contributions to the nonlinear dynamics and control of aerospace structures, including the stability and bifurcations of nonlinear vibration systems under delayed control, the active flutter suppression for aircraft structures, and the deployment dynamics of space structures in orbit. He has authored and co-authored 5 monographs/books and around 300 journal papers, which have been cited over 12,000 times. Prof. Hu received The State Award of Natural Science of China twice and many honors, such as Fellow of Chinese Academy of Sciences in 2007, Fellow of TWAS in 2010, and Honorary Doctor of Science from Moscow State University, Russia in 2015.