Contents1 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 31.2.2 Design of a Hydro-Elastic Vibration Isolation System 71.2.3 Two Kinds of Immovable Points in a Vibration System 101.2.4 Identical Natural Frequencies of Different Structures 131.2.5 Closely Distributed Natural Modes of a SymmetricStructure 161.2.6 Transient Response of a Slender Structure 191.3 Scope and Style of the Book 211.4 Further Reading and Thinking 232 Preparation of Research-Oriented Study 252.1 Briefs of Beauty of Science 252.2 Beautiful Features of Vibration Mechanics 272.2.1 Unity 272.2.2 Simplicity 292.2.3 Regularity 312.2.4 Symmetry 352.2.5 Singularity 392.3 Enlightenment of Beauty of Vibration Mechanics 432.3.1 Methods of Thinking 432.3.2 Aesthetic Literacy 482.4 Concluding Remarks 492.5 Further Reading and Thinking 503 Models of Vibration Systems 513.1 Continuous Systems and Their Discrete Models 523.1.1 Dynamic Models of Continuous Systems 523.1.2 Preconditions of Discretization 593.1.3 Case Studies of Discretization 653.1.4 Concluding Remarks 713.2 A Half Degree of Freedom of Discrete Systems 723.2.1 Degeneration of a Degree of Freedom 733.2.2 Conventional Concept of Degree of Freedom 743.2.3 Degree of Freedom Based on Accessible Manifolds 763.2.4 Demonstrative Systems with a Non-holonomic Constraint 803.2.5 Demonstrative Systems with Two Non-holonomic Constraints 873.2.6 Concluding Remarks 943.3 Structural Damping 953.3.1 Frequency-Invariant Damping and Its Limitations 963.3.2 Frequency-Variant Damping Model and System Response 993.3.3 An Approximate Viscous Damping Model 1013.3.4 An Approximate Viscoelastic Damping Model 1033.3.5 Concluding Remarks 1103.4 Further Reading and Thinking 1104 Vibration Analysis of Discrete Systems 1134.1 Vibration Systems with Non-holonomic Constraints 1144.1.1 Dynamic Analysis in Time Domain 1144.1.2 Dynamic Analysis in Frequency Domain 1264.1.3 Concluding Remarks 1304.2 Node Number of a Natural Mode Shape 1314.2.1 Reexamination of Current Results 1324.2.2 Rules of Node Numbers of 2-DoF Systems 1374.2.3 Design Feasibility of Nodes in a Mode Shape 1424.2.4 Concluding Remarks 1454.3 Anti-resonances of a Harmonically Excited System 1454.3.1 Anti-resonances of 2-DoF Systems 1474.3.2 Mechanisms Behind Two Kinds of Anti-resonances 1484.3.3 Design Feasibility of Anti-resonances 1524.3.4 Concluding Remarks 1584.4 Dynamic Modifications of a System 1584.4.1 Frequency Response of a Composite System 1594.4.2 Adjusting an Anti-resonance of a Primary System 1624.4.3 Adjusting Resonances of a Primary System 1654.4.4 Concluding Remarks 1724.5 Further Reading and Thinking 1735 Natural Vibrations of One-Dimensional Structures 1755.1 Natural Vibrations of a Tether Pendulum 1755.1.1 Dynamic Equation of a Tether Pendulum 1765.1.2 Analysis of Natural Vibrations 1785.1.3 Comparison Between Continuous Model and Discrete Models 1855.1.4 Concluding Remarks 1885.2 Duality Analysis of Rods in Natural Vibrations 1895.2.1 A Dual of Different Cross-Sections 1905.2.2 A Dual of Identical Cross-Sections 1955.2.3 A Dual of Two Uniform Rods 1995.2.4 A Dual of Two Rods with Axially Varying Material Properties 2015.2.5 Concluding Remarks 2045.3 Duality Analysis of Beams in Natural Vibrations 2045.3.1 A Dual of Different Cross-Sections 2065.3.2 A Dual of Identical Cross-Sections 2135.3.3 A Dual of Two Uniform Beams 2205.3.4 Concluding Remarks 2235.4 Further Reading and Thinking 2256 Natural Vibrations of Symmetric Structures 2276.1 Natural Vibrations of Mirror-Symmetric Structures 2286.1.1 Decoupling of Mirror-Symmetric Structures 2286.1.2 Free Vibrations of Thin Rectangular Plates 2376.1.3 Repeated Natural Frequencies of a Thin Rectangular Plate 2426.1.4 Close Natural Frequencies of a Thin Rectangular Plate 2526.1.5 Concluding Remarks 2616.2 Vibration Computations of Cyclosymmetric Structures 2616.2.1 Decoupling a Cyclosymmetric Structure Without a Central Axis 2646.2.2 Decoupling a Cyclosymmetric Structure with a Central Axis 2806.2.3 High-Efficient Computation Based on Modal Reduction 2896.2.4 Concluding Remarks 2976.3 Modal Properties of Cyclosymmetric Structures 2976.3.1 Modal Properties in Representative Subspaces of Cyclic Group 2986.3.2 Modal Properties in Physical Space 3016.3.3 Central Displacements in Mode Shapes 3076.3.4 Orthogonality of Mode Shapes with Repeated Frequencies 3146.3.5 Modal Test of a Bladed Disc Model 3186.3.6 Concluding Remarks 3216.4 Further Reading and Thinking 3227 Waves and
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