اسم المؤلف
Keith L. Richards
التاريخ
14 نوفمبر 2020
المشاهدات
التقييم
(لا توجد تقييمات)

Design Engineer’s Reference Guide
Mathematics, Mechanics, and Thermodynamics
Keith L. Richards
Contents
Preface xv
Author xvii
Acknowledgement .xix
Chapter 1 Mathematics .1
1.1 Trigonometry .1
1.1.1 Right-Angled Triangle 1
1.1.2 Oblique-Angled Triangles 2
1.1.3 Trigonometric Relations .2
1.2 Hyperbolic Functions 3
1.2.1 Inverse Hyperbolic Functions 3
1.3 Solution of the Quadratic Equation .4
1.4 Solution of Simultaneous Equations (Two Unknowns) .4
1.5 Laws of Exponents 4
1.6 Expansions .5
1.7 Real Root of the Equation f(x) = 0 Using the Newton–Raphson Method .5
1.8 Series .6
1.9 Logarithms 6
1.10 Differential Calculus .7
1.11 Integral Calculus .7
1.11.1 Integration Is the Inverse of Differentiation .7
1.11.2 Indefinite Integrals . 10
1.11.3 Determination of an Area 10
1.11.4 Approximate Integration 12
1.12 Laplace Transforms . 13
1.12.1 First Derivative . 14
1.12.2 Second Derivative 14
1.12.3 Higher Derivatives . 15
1.13 Parallel Axis Theorem . 15
1.13.1 Calculation of the Moment of Inertia Using the Parallel
Axis Theorem . 15
1.14 Complex Numbers . 17
1.14.1 Introduction 17
1.14.2 Argand Diagram . 18
1.14.3 Manipulation of Complex Numbers . 19
1.14.3.2 Multiplication 19
1.14.3.3 Division .20
1.14.4 Polar Form of a Complex Number .20
1.14.5 Exponential Form of a Complex Number 22
1.15 Determinates .23
1.15.1 Introduction 23
1.15.2 Description .23
1.15.3 Determinant Order .24
1.15.4 Properties of the Determinant 24vi Contents
1.15.5 Minors and Cofactors .25
1.16 Matrices .25
1.16.1 Introduction 25
1.16.2 Definitions 25
1.16.2.1 Square Matrix .26
1.16.2.2 Row Matrix .26
1.16.2.3 Column Matrix .26
1.16.2.4 Diagonal Matrix 26
1.16.2.5 Unit Matrix .26
1.16.2.6 Symmetric Matrix 27
1.16.2.7 Skew Symmetric Matrix—That Is, Anti-Symmetric
(aij = −aji) .27
1.16.2.8 Null Matrix .27
1.16.3 Matrix Algebra .27
1.16.3.2 Multiplication of Matrices 27
1.16.3.3 Transposition of a Matrix .28
1.16.3.4 Adjoint of a Matrix .28
1.16.3.5 Inverse of a Square Matrix .28
1.16.3.6 Transformation from Cylindrical Coordinates to
Cartesian Coordinates 28
Chapter 2 Introduction to Numerical Methods .29
2.1 Introduction .29
2.2 Numerical Methods for Integration .29
2.2.1 Manual Method 30
2.2.2 Mid-Ordinate Rule .30
2.2.3 Trapezoidal Rule 32
2.2.4 Simpson’s Rule .34
2.3 Evaluation of Errors .36
2.4 Round-Off and Truncation Errors .36
2.4.1 Round-Off Errors .36
2.4.2 Truncation Errors .36
2.5 Errors Arising from Differentiation 38
2.6 Integration Errors 38
2.7 Series .39
2.8 Newton–Raphson Method .39
2.8.1 Demonstration of the Method 39
2.9 Iterative Methods for Solving Linear Equations . 41
2.9.1 Gauss Elimination Method 41
2.9.2 Jacobi Iterative Method 41
2.9.3 Gauss–Seidel Method . 45
2.10 Non-Linear Equations . 47
2.10.1 Newton’s Method 47
Chapter 3 Properties of Sections and Figures . 51
3.1 Centroid C
x, Cy, Cz . 51
3.2 Moment of Inertia/Second Moment of Area . 51
3.3 Polar Moment of Inertia of a Plane Area 51Contents vii
Chapter 4 Statics . 57
4.1 Force, Mass and Moments . 57
4.1.1 System of Units 58
4.1.2 Free-Body Diagrams 58
4.1.3 Forces and Moments 58
4.1.3.1 Force .58
4.1.3.2 Moments .59
4.1.3.3 Couples .60
4.1.3.4 Rigid-Body Equilibrium .60
4.2 Structures .60
4.2.1 Pin Joint 62
4.2.1.1 Struts and Ties 62
4.2.1.2 Bow’s Notation 62
4.2.2 Solving Forces in Pin-Jointed Frames 64
4.2.3 Method of Joints .66
4.2.4 Graphical Methods as Applied to a 2-Dimensional Framework 66
4.2.5 Method of Sections as Applied to a Plane Framework 67
4.3 Vectors and Vector Analysis .70
4.3.2 Vector Subtraction 70
4.3.3 Resolving a Vector into Components .70
4.3.4 Analytical Determination of the Components of the Vector . 71
4.3.5 Resultant of a Number of Coplanar Vectors (More than
Two Vectors) .72
4.3.6 Analytical Solution to Figure 4.22 .73
4.3.7 Product of Vectors 73
4.3.7.1 Multiplication of a Vector ‘P’ by a Scalar ‘K’ 73
4.3.7.2 Scalar Product of Two Vectors .73
4.3.8 Vector (or Cross) Product . 74
Chapter 5 Dynamics . 75
5.1 Kinematics . 75
5.2 Nomenclature . 75
5.3 Newton’s Laws of Motion (Constant Acceleration) . 75
5.3.1 Linear Motion Equations 75
5.3.2 Angular Motion Equations . 76
5.4 Rectilinear Motions . 76
5.4.1 Uniform Linear Motion 76
5.4.2 Non-Uniform Linear Motion 77
5.4.3 Variable Velocity 77
5.4.4 Variable Acceleration .77
5.5 Circular Motion . 78
5.5.1 Motion on a Circular Path 78
5.5.2 Rolling Wheel 79
5.6 Absolute and Relative Motion .79
5.7 Rotating Unit Vector 79
5.8 Vector of Point in a Rotating Reference Frame .80
5.9 Velocity of a Point in a Moving Reference Frame 81
5.10 Acceleration of a Particle 82
5.11 Kinematics of Rigid Bodies in One Plane .82viii Contents
5.12 Instantaneous Centre of Rotation 83
5.13 Kinematics of Rigid Bodies in Three Dimensions 84
5.14 Theorems .84
5.15 Translation Motion 85
5.16 Rotation about a Fixed Axis 85
5.17 Rotation about a Fixed Point .86
5.18 General Motion 87
Chapter 6 Mechanical Vibrations .89
6.1 Introduction .89
6.2 Single Degree of Freedom: Free Vibrations 89
6.2.1 Free Natural Vibrations 89
6.2.2 Simple Harmonic Motion . 91
6.2.2.1 Angular Frequency, Frequency and Periodic Time 92
6.2.2.2 Equations for SHM .93
6.2.2.3 Free Natural Vibrations of a Single-Degree-ofFreedom System .95
6.2.2.4 Elementary Parts of a Vibrating System 97
6.2.2.5 Linear Elastic Oscillations 97
6.2.2.6 Transverse Vibrations .99
6.2.2.7 Energy Methods (Rayleigh) 102
6.3 Damped Vibrations 105
6.3.1 Viscous Damping . 106
6.3.2 Coulomb Damping . 111
6.3.3 Inertial Damping 112
6.3.4 Internal Damping . 112
6.4 Single Degree of Freedom: Forced Vibrations 113
6.4.1 Forced Vibrations . 114
6.4.1.1 Disturbing Force Acting on Mass . 114
6.4.1.2 Phasor Representation 115
6.5 Natural Frequency of Beams and Shafts . 116
6.5.1 Degrees of Freedom . 117
6.5.2 Beams Subject to Transverse Vibrations 118
6.5.3 Simply Supported Beam Subject to Transverse Vibration . 118
6.5.4 Torsional Frequency of a Cantilevered Shaft Carrying a Mass
at the Free End . 118
6.5.5 Torsional Frequency of a Shaft Carrying Two Masses 119
6.5.6 Torsionally Equivalent Shafts 120
6.5.7 Torsional Frequency of a Geared Shaft Carrying
Two Masses 123
6.5.8 Torsional Frequency of a Shaft Carrying Three Masses . 128
6.6 Forced Vibrations 129
6.6.1 Overview 129
6.6.2 External Forcing . 130
6.6.3 Frequency Response Diagrams 132
6.6.4 Harmonic Movement of the Support 136
6.6.5 Magnification Factor 137
6.6.6 Transmissibility 140
6.6.7 Using Forced Vibration Response to Measure the Properties
of a Structure 141Contents ix
Chapter 7 Introduction to Control Systems Modelling . 145
7.1 Introduction . 145
7.1.1 Basics of Control Theory . 145
7.1.2 Open-Loop Control System . 145
7.1.3 Closed-Loop Control System . 146
7.1.4 Control System Definitions 146
7.1.4.1 System . 146
7.1.4.2 Input 146
7.1.4.3 Output . 147
7.1.4.4 Open Loop 147
7.1.4.5 Closed Loop 147
7.1.4.6 Feedback . 147
7.1.4.7 Servomechanism . 147
7.1.4.8 Regulator . 147
7.1.5 Feedback Characteristics 147
7.1.6 Control Models . 148
7.1.7 Block Diagrams and Transfer Functions 148
7.2 Engineering System Models 149
7.2.1 Similarities of Elements between Systems . 149
7.2.1.1 Capacitance . 149
7.2.1.2 Resistance . 150
7.2.1.3 Inductance, Inertia and Inertance . 150
7.2.1.4 Other Symbols Used . 150
7.2.2 Laplace Transforms 150
7.2.3 Transfer Functions 150
7.2.4 Linear Mechanical Systems . 151
7.2.4.1 Spring 151
7.2.4.2 Damper or Dashpot . 151
7.2.4.3 Mass 152
7.2.4.4 Mass–Spring System 152
7.2.4.5 Spring–Damper System 154
7.2.4.6 Mass–Spring–Damper System . 155
7.2.5 Rotary Mechanical Systems . 157
7.2.5.1 Torsion Bar 157
7.2.5.2 Torsion Damper 158
7.2.5.3 Moment of Inertia . 158
7.2.5.4 Geared Systems 158
7.2.6 Thermal Systems 162
7.2.6.1 Heating and Cooling . 162
7.2.6.2 Process Heating System 164
7.2.7 Hydraulic System . 166
7.2.7.1 Hydraulic Motor . 166
7.2.7.2 Hydraulic Cylinder . 168
7.2.7.3 Directional Valve and Actuator 169
7.2.7.4 Directional Control Valve and Actuator Connected
to a Mass . 171
7.2.8 Electrical System Models . 174
7.2.8.1 Resistance . 174
7.2.8.2 Capacitance . 175
7.2.8.3 Inductance . 176x Contents
7.2.8.4 Potentiometer 176
7.2.8.5 R–C Series Circuit 177
7.2.8.6 L–C–R in Series . 178
7.2.9 Closed-Loop System Transfer Function with a Unity Feedback . 179
7.3 Block Diagram and Transfer Function Manipulations 181
7.3.1 Open-Loop Control System . 181
7.3.2 Closed-Loop Control System . 181
7.3.3 Summing Junctions 182
7.3.4 Closed-Loop System Transfer Functions . 183
7.3.5 Velocity Feedback 185
7.3.6 Disturbance 186
7.3.6.1 To Eliminate the Effect of a Disturbance . 188
7.3.7 Proportional and Differential Control 188
7.3.8 Simplifying Complex Systems . 190
Chapter 8 Heat and Temperature 193
8.1 Heat 193
8.1.1 Temperature 193
8.1.1.1 Temperature Scales . 193
8.1.2 Thermal Expansion 194
8.1.3 Heat Capacity . 196
8.1.4 Heat Transfer 197
8.1.4.1 Conduction 197
8.1.4.2 Convection 198
Chapter 9 Thermodynamic Basics 201
9.1 Introduction . 201
9.1.1 What Is Thermodynamics? 201
9.1.2 Brief History . 201
9.2 Basic Thermodynamics . 201
9.2.1 Basic Concepts . 201
9.2.2 Extensive 202
9.2.3 Intensive .202
9.2.4 Specific and Total Quantities .203
9.2.5 Energy Forms .203
9.2.6 Internal Energy .203
9.2.7 Gravitational or Potential Energy .203
9.2.8 Kinetic Energy .204
9.2.9 Flow Energy .204
9.2.10 Enthalpy .204
9.2.11 Gas Laws 205
9.2.12 Theory 205
9.2.13 Pressure 205
9.2.14 A Perfect Gas .205
9.2.15 Boyle’s Law 206
9.2.16 Charles’s Law .207
9.2.17 Universal Gas Law .208
9.2.18 Specific Heat Capacity . 210
9.2.19 Specific Heat Capacity at Constant Volume (Cv) . 211Contents xi
9.2.20 Specific Heat Capacity at Constant Pressure (Cp) 212
9.2.21 Relationship between the Specific Heats . 213
9.2.22 Specific Heat Ratio ‘γ’ . 214
9.3 Laws of Thermodynamics . 215
9.3.1 Conservation of Energy 215
9.3.2 First Law of Thermodynamics . 215
9.3.3 Steady Flow Process . 215
9.3.4 Flow Process 215
9.3.5 Consider a Boiler at Constant Pressure 216
9.3.6 Nozzle . 218
9.3.7 Pump 220
9.3.8 Turbine 221
9.3.9 Throttling .222
9.3.10 Equation of Continuity .224
9.3.11 Non-Flow Processes .224
9.3.12 Constant Temperature (Isothermal) Process (pV – C) .225
9.3.12.1 Work Transfer .226
9.3.12.2 Heat Transfer 226
9.3.13 Adiabatic Process (Q = 0) .227
9.3.13.1 Work Transfer .228
9.3.13.2 Heat Transfer 229
9.3.14 Polytropic Process (pVn = C) 230
9.3.14.1 Work Transfer . 231
9.3.14.2 Heat Transfer 232
9.3.15 Constant Volume Process . 233
9.3.15.1 Work Transfer .234
9.3.15.2 Heat Transfer 234
9.3.16 Constant Pressure Process 235
9.3.16.1 Work Transfer .236
9.3.16.2 Heat Transfer 236
Chapter 10 Fluid Mechanics . 239
10.1 Fluid Properties . 239
10.1.1 Density 239
10.1.2 Pressure 240
10.1.3 Static Pressure and Head 241
10.1.4 Viscosity .242
10.1.4.1 Coefficient of Dynamic Viscosity 243
10.1.4.2 Kinematic Viscosity .243
10.1.4.3 Other Units .243
10.1.5 Compressibility 243
10.2 Fluid Flow 244
10.2.1 Patterns of Flow .244
10.2.2 Types of Flow .244
10.2.2.1 Internal Flow 244
10.2.2.2 External Flow .244
10.2.2.3 Laminar Flow .245
10.2.2.4 Turbulent Flow 245
10.2.3 Laminar Flow .245
10.2.4 Derivation of Poiseuille’s Equation for Laminar Flow 246xii Contents
10.2.5 Turbulent Flow .250
10.2.6 Fluid Resistance . 251
10.2.7 Moody’s Diagram . 252
10.3 Continuity Equation 254
10.3.1 Conservation of Mass .254
10.3.2 Conservation of Energy 255
10.3.2.1 Flow Energy 255
10.3.2.2 Potential Energy . 255
10.3.2.3 Kinetic Energy 255
10.3.2.4 Specific Energy .256
10.3.3 Bernoulli’s Equation .256
10.3.4 Stagnation Point .259
10.4 Hydrostatics .260
10.4.1 Buoyancy 260
10.4.2 Metacentre and Metacentre Height 262
10.4.3 Pressure in Liquids .264
10.4.4 Pressure Due to the Weight of a Liquid . 267
10.4.5 Forces on Submerged Surfaces 269
10.4.6 Centre of Pressure 270
10.5 Dimension Analysis . 273
10.5.1 Dimensions . 273
10.5.2 Dimensional Equations 274
10.6 Fluid Drag 275
10.6.1 Form Drag 275
10.6.2 Skin Friction Drag 276
10.6.3 Estimating Skin Drag .277
10.6.4 General Notes on Drag Coefficients 278
10.6.5 Total Drag .280
10.6.6 Drag on a Cylinder . 281
10.7 Properties of Water 284
10.7.1 Specific Heat Capacity of Water 286
10.7.2 Enthalpy of Fusion .287
10.7.3 Enthalpy of Vaporisation 287
10.8 Channel Flow .288
10.8.1 Channel Flow .288
10.8.3 Flow Rate .289
10.8.4 Roughness 290
10.9 Orifice Plate .292
10.9.1 Description .292
10.9.2 Measurement 293
10.10 Fluid Machines 294
10.10.1 Positive Displacement Machines 294
10.10.1.1 Single Rotor 294
10.10.1.2 Double Rotor .296
Chapter 11 Introduction to Linkages 301
11.1 Introduction . 301
11.2 Brief History 301Contents xiii
11.3 Kinematic Definitions .302
11.3.1 Kinematic Chain 302
11.3.2 Mechanism .302
11.3.3 Machine 302
11.3.4 DOF 302
11.3.6 Order of a Link .303
11.3.7 Joints .303
11.3.8 Kinematic Pairs 303
11.3.9 Mobility 304
11.4 Kinematic Pairs .304
11.4.1 Relative Motion between Kinematic Pairs .304
11.4.1.1 Lower Pairs .304
11.4.1.2 Higher Pairs 305
11.4.2 Nature of Kinematic Constraints .306
11.4.3 Closed Pair .306
11.4.4 Open Pair 306
11.5 Planar, Spherical and Spatial Mechanisms .307
11.5.1 Planar Mechanism 307
11.5.2 Spherical Mechanism .307
11.5.3 Spatial Mechanism .308
11.6 Mobility .309
11.7 Chebyshev–Gruber–Kutzbach Criterion .309
11.8 Grashof’s Law 310
11.8.1 Classification 311
11.9.2 Inversion . 313
11.9.3.1 Link 1 Fixed . 315
11.9.3.2 Link 2 Fixed . 315