Applied Solid Dynamics

1 Introduction 1.1 Historical Review 1.2 Newton's Three Laws of Motion 1.2.1 Basic Vehicle Dynamics Problem 1.2.2 Basic Linear Vibration Problem (Single Degree of Freedom) Problems2 Power Transmission through Gear Systems 2.1 Introduction 2.2 General Spur Gear Systems 2.2.1 Kerr Diagram for Determining Speed Ratios 2.3 Epicyclic Gear System 2.3.1 Automobile 'Overdrive' Unit Problems 3 Dynamics of a Solid Body in General Plane Motion 3.1 Kinematics of General Plane Motion 3.2 Kinetics of General Plane Motion Problems 4 Turning Moment Diagrams and Flywheel Design 4.1 Turning Moment Diagrams 4.1.1 Complete System Cycle Angle 4.1.2 Complete System Turning Moment Diagram 4.2 Flywheel Design 4.2.1 Solid Circular Flywheel 4.2.2 Annular (Or Ring) Flywheel 4.2.3 Additional Design Considerations Problems 5 Applications of Friction 5.1 Introduction 5.1.1 Forces Preventing Slip 5.1.2 Friction Forces Acting on Moving Bodies 5.2 Belt Drive Systems 5.2.1 Flat-Form Belts 5.2.2 V-Form Belts 5.3 Clutch Drive Mechanism 5.3.1 Annular Contact Clutch 5.3.2 Conical Contact Clutch 5.4 Friction Brake Mechanisms 5.4.1 Shoe Brakes 5.4.2 Disc Brakes Problems 6 Out-Of-Balance and Balancing of Rotating Mass Systems 6.1 Introduction 6.2 Out-of-Balance Forces and Moments 6.3 Balancing of Frame Forces and Frame Force Moments 6.4 Experimental Method for Balancing of Rotodynamic Machinery 6.4.1 Single-Plane Balancing 6.4.2 Two-Plane Balancing Problems 7 Out-Of-Balance and Balancing of Reciprocating Mass Systems 7.1 Introduction 7.2 Out-of-Balance Frame Forces and Moments 7.3 Regular In-Line Vertical Cylinder Engines 7.3.1 Four-Cylinder Engine 7.3.2 Five-Cylinder Engine 7.3.3 Six-Cylinder Engine 7.4 Regular Off-line Cylinder Engines 7.4.1 The Flat-Four Boxer Engine 7.4.2 V8 Engine 7.5 Balancing of Primary Frame Force and Frame Force Moment Problems 8 Introduction to Dynamics of General Space Motion 8.1 Introduction 8.2 Kinematic Analysis 8.2.1 Velocity Vectors 8.2.2 Acceleration Vectors 8.3 Kinetic Analysis 8.3.1 Force and Moments 8.3.2 Momentum and Moment of Momentum 8.3.3 Solid Uniform Disc Spinning About Its Central Axis 8.3.4 Solid Uniform Spinning Disc Undergoing Uniform Precession at Constant Nutation 8.4 Gyroscopes and Gyroscopic Torque 8.4.1 Uniform Precession at an Angle of Nutation O = 0¢X 8.4.2 Uniform Precession at an Angle of Nutation O = 90¢X Problems 9 Vibration of a Single Degree of Freedom System 9.1 Introduction 9.2 Series and Parallel Stiffness Arrangements 9.2.1 Stiffnesses in Series 9.2.2 Stiffnesses in Parallel 9.3 Free Vibration of an Undamped System 9.4 Free Vibration of Damped Systems 9.4.1 Vibratory Response 9.4.2 Analysis of Transient Waveform 9.5 Forced Vibration 9.5.1 Steady-State Vibratory Response 9.5.2 Rotational Out-of-Balance 9.5.3 Foundation Force and Transmissibility 9.5.4 Seismic Excitation and Seismic Instruments Problems 10 Free Undamped Vibration of a Two Degree of Freedom System 10.1 Introduction 10.2 Rectilinear Systems 10.3 Torsional Systems 10.3.1 General Analysis 10.3.2 Two-Rotor Single-Stiffness Systems 10.3.3 Mode of Angular Oscillation 10.3.4 Non-Uniform Shaft Systems 10.3.5 Torsional Vibration of a Geared Two-Rotor System Problems 11 Vibration of Multiple Degree of Freedom Lumped Mass Systems—Matrix Analysis 11.1 Introduction 11.2 Undamped Natural Frequencies and Associated Normal Modes (Eigenvalues and Eigenvectors) 11.2.1 Orthogonal Properties of Eigenvectors 11.3 Response of Undamped and Damped Systems—Modal Analysis 11.3.1 Steady-State Response to Harmonic Forcing 11.3.2 Transient Response of Damped Systems 11.4 Experimental Determination of Modal Parameters Problems 12 Free Vibration of Continuous Systems 12.1 Introduction 12.2 Transverse Vibration of a String or Cable 12.3 Longitudinal Vibration of a Prismatic Bar 12.4 Torsional Vibration of a Uniform Circular Bar 12.5 Transverse Vibration of a Prismatic Beam 12.5.1 Effects of Rotary Inertia and Shear Deformation 12.5.2 Transverse Vibration of a Rotating Beam 12.6 Energy Methods 12.6.1 Rayleigh Method 12.6.2 Ritz Method 12.7 Whirling of Shafts Problems13 Introduction to Vibratory Control 13.1 Introduction 13.2 Active Vibratory Control 13.3 Passive Vibratory Control 13.3.1 Nodalized Beam Isolator 13.3.2 Dynamic Anti-Resonant Vibration Isolator (Davi) 13.3.3 Tuned Absorber Appendix 1 Standard Integrals Appendix 2 Basic Complex Algebra Appendix 3 Basic Vector Algebra Index