Note: Cover -- Contents -- Preface -- Chapter One Introduction -- 1.1 What Is Vibration? -- 1.2 Classification of Vibration Studies -- (1) Vibration Analysis -- (2) System Design -- (3) Input Evaluation -- (4) System Identification -- 1.3 Classification of Vibration -- (1) Classification Based on Input -- (2) Classification Based on Output -- (3) Classification Based on the Degrees of Freedom of the System -- (4) Classification Based on Differential Equation of Motion of the System -- 1.4 Harmonic Vibration -- 1.5 Harmonic Analysis -- Problems -- References -- Chapter Two Vibration of a Single-Degree-of-Freedom System -- 2.1 Introduction: Modeling -- 2.2 Free Vibration of a Single-Degree-of-Freedom System -- (1) Governing Differential Equation of Motion -- (2) Equivalent Spring Stiffness -- 2.3 The Energy Method -- (1) The Law of Conservation of Energy -- (2) The Rayleigh Method -- 2.4 Effective Mass -- 2.5 Damped Free Vibration of a Single-Degree-of-Freedom System -- (1) Damping Forces -- (2) Differential Equation of Motion -- (3) Discussion of the Solution -- Problems -- References -- Chapter Three Harmonically Excited Motion -- 3.1 Introduction -- 3.2 Forced Harmonic Vibration of Damped Systems -- 3.3 Forced Harmonic Vibration of Undamped Systems -- (1) Beating -- (2) Resonance -- 3.4 Forced Vibration Caused by Rotating Unbalance -- 3.5 Forced Vibration Caused by Support Motion -- 3.6 Vibration Isolation -- (1) Isolation of the Machine from the Foundation -- (2) Isolation of the Foundation from the Machine -- 3.7 Damping -- (1) Energy Dissipation Due to a Viscous Damping Force -- (2) Structural (Hysteretic) Damping -- (3) Complex Stiffness and Lost Factor -- (4) Sharpness of Resonance -- 3.8 Forced Vibration Under Periodic Excitation -- 3.9 Response to Arbitrary Excitation -- Problems -- References -- Chapter Four Balancing of Rotors. , 4.1 Unbalance -- (1) Static Unbalance -- (2) Dynamic Unbalance -- 4.2 Whirling of Rotating Shaft -- 4.3 Experimental Balancing -- (1) The Influence Coefficient Method: Single-Plane Balancing -- (2) The Influence Coefficient Method: Two-Plane Balancing -- 4.4 Inertia Forces in a Single-Cylinder Engine -- 4.5 Inertia Forces and Couples of Multicylinder Engines -- 4.6 Balancing of Crankshafts -- Problems -- References -- Chapter Five Multi-Degree-of-Freedom Systems -- 5.1 Introduction -- 5.2 Two-Degree-of-Freedom Systems -- (1) Equations of Motion -- (2) Characteristic Equation and Natural Frequency -- (3) Mode Shapes -- 5.3 Eigenvalues and Eigenvectors -- 5.4 Orthogonal Properties of the Modal Vectors -- 5.5 Zero Eigenvalues and Repeated Roots -- (1) Zero Eigenvalues -- (2) Repeated Roots -- 5.6 Response of a System to Initial Conditions -- 5.7 Coordinate Coupling -- 5.8 Undamped Systems and Coordinate Decoupling -- (1) Forced Response and Coordinate Decoupling -- (2) Initial Value Problem and Coordinate Decoupling -- 5.9 Damped Systems and Coordinate Decoupling -- (1) Coordinate Decoupling with Forced Response -- (2) Coordinate Decoupling with Initial Value Problems -- 5.10 Lagrange's Equations -- (1) Generalized Coordinates and Virtual Displacements -- (2) Virtual Work and Generalized Forces -- (3) Lagrange's Equations -- 5.11 Kane's Equations -- (1) Partial Velocities and Partial Angular Velocities -- (2) Inertia Forces -- (3) Generalized Applied Forces -- (4) Kane's Equations -- Problems -- References -- Chapter Six Numerical Methods -- 6.1 Introduction -- 6.2 Various Eigenvalue Analyses -- (1) The Generalized Eigenvalue Problem -- (2) The Algebraic Eigenvalue Problem -- (3) The Symmetric Eigenvalue Problem -- (4) The Standard Eigenvalue Problem in State Space -- (5) The Generalized Eigenvalue Problem in State Space. , 6.3 Numerical Evaluation of the Time Response -- Problems -- References -- Chapter Seven Transfer Functions and Frequency Response Functions -- 7.1 Introduction -- 7.2 The Laplace Transformation and Fourier Transformation -- (1) The Laplace Transform -- (2) The Fourier Transform -- 7.3 Laplace Domain: Transfer Function -- 7.4 Frequency Domain: Frequency Response Function -- (1) Receptance (or Admittance, or Dynamic Compliance) -- (2) Mobility -- (3) Accelerance (or Inertance) -- (4) The Bode Diagrams -- (5) The Nyquist Diagrams -- 7.5 Time Domain: Impulse Response Function -- 7.6 FRFs of Multi-Degree-of-Freedom Systems -- (1) Laplace Domain: Transfer Function Matrix -- (2) Frequency Domain: Frequency Response Function Matrix -- (3) Time Domain: Impulse Response Functions -- 7.7 Determination of Residues and Poles in State Space -- Problems -- References -- Chapter Eight Lumped Parameter Systems -- 8.1 Introduction -- 8.2 The Flexibility and Stiffness Matrices -- 8.3 Maxwell's Reciprocity Theorem -- 8.4 Eigenvalue Analysis -- 8.5 Dunkerley's Equation -- 8.6 Rayleigh Principle -- 8.7 Method of Matrix Iteration -- 8.8 Determining of Higher-Order Modes and Frequencies -- 8.9 Transfer Matrix Method -- (1) A Spring-Mass System -- (2) Torsional Systems -- (3) A Geared System -- (4) Branched Systems -- 8.10 Beams Modeled as Lumped Masses -- (1) Flexural Vibration -- (2) Rotating Beams -- Problems -- References -- Chapter Nine Continuous Systems -- 9.1 Introduction -- 9.2 Lateral Vibration of a String -- (1) d'Alembert's Solution -- (2) Separation of Variables -- 9.3 Longitudinal Vibration of Rods -- 9.4 Torsional Vibration of Rods -- 9.5. Lateral Vibration of Beams -- 9.6 Orthogonal Relations -- 9.7 Effects of Rotary Inertia, Shear, and Axial Loading -- (1) The Effect of Rotary Inertia and Shearing Deformation. , (2) The Effect of Axial Force on Lateral Vibration -- 9.8 Forced Vibration -- 9.9 Ritz Method -- Problems -- References -- Chapter Ten Engine Mounting Systems -- 10.1 Introduction -- 10.2 Inertia Properties of an Engine -- (1) Reference Frame and Direction Cosines -- (2) Inertia Matrix -- (3) Mass Center -- 10.3 Orientation Angles and Transformation Matrix -- 10.4 Equations of Motion -- (1) Forces and Torques Produced by an Engine Mount due to Translational Motion of the Engine -- (2) Forces and Torques Produced by an Engine Mount due to Rotational Motion of the Engine -- 10.5 Mode Shapes and Natural Frequencies -- 10.6 Decoupling and Optimization -- (1) Two-Degree-of-Freedom Coupled System -- (2) Three-Degree-of-Freedom Coupled System -- (3) Optimization -- 10.7 Torque Roll Axis (TRA) -- 10.8 Torque Roll Axis (TRA) Mode Decoupling -- Problems -- References -- Chapter Eleven Experimental Modal Analysis -- 11.1 Introduction -- 11.2 Modal Analysis Theory -- 11.3 The Complex Exponential Algorithm -- 11.4 The Least-Squares Complex Exponential Method -- 11.5 The Polyreference Time Domain Method -- 11.6 The Ibrahim Time Domain Method -- 11.7 The Eigensystem Realization Algorithm -- 11.8 Estimation of Modal Vectors -- 11.9 Estimation of Frequency Response Functions -- (1) Ĥ1 Estimator of FRF -- (2) Ĥ2 Estimator of FRF -- (3) Ĥv Estimator of FRF -- 11.10 Coherence Function -- (1) Ordinary Coherence Function -- (2) Multiple Coherence Function -- (3) Partial Coherence Function -- 11.11 Discrete Fourier Transfer (DFT) and Fast Fourier Transfer (FFT) -- (1) Aliasing -- (2) Leakage -- 11.12 Window Functions -- 11.13 Averaging -- (1) Linear Average -- (2) Stable Average -- 11.14 Overlapping Signal Analysis -- 11.15 Modal Data Acquisition -- (1) Test Structure -- (2) Exciter -- (3) Data Acquisition System -- (4) Analyzer -- 11.16 Operational Modal Analysis. , (1) Stochastic Subspace Identification Method -- (2) The Natural Excitation Technique (NExT) -- 11.17 Running Modes Analysis -- Problems -- References -- Chapter Twelve Special Topics -- 12.1 Introduction -- 12.2 Complex Structure Analysis Using the FRFs of Substructures -- (1) Equations of Motion -- (2) Solution Method -- 12.3 Translational Vibration Absorber -- (1) Absorber Tuning Based on the Primary System FRF -- (2) Special Cases: A Single-Degree-of-Freedom System -- 12.4 Torsional Vibration Absorber -- 12.5 Experimental Measurement of the Torsional FRF -- 12.6 HYFEX Method -- 12.7 Sensitivity Analysis -- (1) Eigenvalue Derivatives -- (2) Eigenvector Derivatives -- References -- Appendix A -- Appendix B -- Appendix C -- Notation -- Index.