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## Engineers Guide to MATLAB

### Introduction

For undergraduate engineering courses in Mechanical, Aeronautical, Civil, and Electrical engineering that require/use MATLAB. An authoritative guide to generating readable, compact, and verifiably correct MATLAB programs.

This highly respected guide helps students develop a strong working knowledge of MATLAB that can be used to solve a wide range of engineering problems. Since solving these problems usually involves writing relatively short, one-time-use programs, the authors demonstrate how to effectively develop programs that are compact yet readable, easy to debug, and quick to execute. Emphasis is on using MATLAB to obtain solutions to several classes of engineering problems, so technical material is presented in summary form only.

Advanced Methods of Structural Analysis

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### Table Of Contents

1 Introduction 1

Edward B. Magrab

1.1 Introduction 1

1.1.1 Organization of the Book and Its Goals 2

1.1.2 Some Suggestions on How to Use MATLAB 2

1.1.3 Book Notation Conventions 3

1.2 The MATLAB Environment 3

1.2.1 Introduction 3

1.2.2 Preliminaries–Command Window Management 5

1.2.3 Executing Expressions from the MATLAB Command Window–Basic MATLAB Syntax 8

1.2.4 Clarification and Exceptions to MATLAB’S Syntax 11

1.2.5 MATLAB Functions 14

1.2.6 Creating Scripts and Executing Them from the MATLAB Editor 19

1.3 Online Help 29

1.4 The Symbolic Toolbox 33

1.5 Summary of Functions Introduced in Chapter 1 41

Exercises 42

2 Vectors and Matrices 51

Edward B. Magrab

2.1 Introduction 51

2.2 Definitions of Matrices and Vectors 52

2.3 Creation of Vectors 53

2.4 Creation of Matrices 64

2.5 Dot Operations 83

2.6 Mathematical Operations with Matrices 92

2.6.1 Addition and Subtraction 92

2.6.2 Multiplication 92

2.6.3 Determinants 101

2.6.4 Matrix Inverse 104

2.6.5 Solution of a System of Equations 107

2.7 Summary of Functions Introduced in Chapter 2 112

Exercises 113

3 Data Input/Output 127

Edward B. Magrab

3.1 Strings and Annotated Output 127

3.1.1 Creating Strings 127

3.1.2 Converting Numerical Values to Strings and Displaying Them 130

3.2 Entering Data with input 135

3.2.1 Entering a Scalar with input 135

3.2.2 Entering a String with input 136

3.2.3 Entering a Vector with input 137

3.2.4 Entering a Matrix with input 137

3.3 Input/Output Data Files 137

3.4 Cell Arrays 141

3.5 Input Microsoft Excel Files 143

3.6 Summary of Functions Introduced in Chapter 3 144

Exercises 145

4 Program Flow Control 148

Edward B. Magrab

4.1 Introduction—The Logical Operator 148

4.2 Control of Program Flow 151

4.2.1 Branching—If Statement 151

4.2.2 Branching—Switch Statement 154

4.2.3 For Loop 155

4.2.4 While Loop 162

4.2.5 Early Termination of Either a for or a while Loop 166

4.3 Summary of Functions Introduced in Chapter 4 166

Exercises 167

5 Function Creation and Selected MATLAB Functions 172

Edward B. Magrab

5.1 Introduction 173

5.1.1 Why Use Functions 173

5.1.2 Naming Functions 174

5.1.3 Length of Functions 174

5.1.4 Debugging Functions 174

5.2 User-Defined Functions 175

5.2.1 Introduction 175

5.2.2 Function File 175

5.2.3 Subfunctions 181

5.2.4 Anonymous Functions 183

5.2.5 inline 184

5.2.6 Comparison of the Usage of Subfunctions, Anonymous Functions, and inline 185

5.3 User-Defined Functions, Function Handles, and feval 186

5.4 MATLAB Functions that Operate on Arrays of Data 187

5.4.1 Introduction 187

5.4.2 Fitting Data with Polynomials–polyfit/polyval 188

5.4.3 Fitting Data with spline 190

5.4.4 Interpolation of Data–interp1 192

5.4.5 Numerical Integration–trapz 193

5.4.6 Area of a Polygon–polyarea 195

5.4.7 Digital Signal Processing–fft and ifft 196

5.5 MATLAB Functions that Require User-Defined Functions 201

5.5.1 Zeros of Functions–fzero and roots/poly 202

5.5.2 Numerical Integration–quadl and dblquad 207

5.5.3 Numerical Solutions of Ordinary Differential Equations–ode45 212

5.5.4 Numerical Solutions of Ordinary Differential Equations–bvp4c 217

5.5.5 Numerical Solutions of Delay Differential Equations–dde23 231

5.5.6 Numerical Solutions of One-Dimensional Parabolic—Elliptic Partial Differential Equations–pdepe 233

5.5.7 Local Minimum of a Function–fminbnd 235

5.5.8 Numerical Solutions of Nonlinear Equations–fsolve 238

5.6 Symbolic Solutions and Converting Symbolic Expressions into Functions 240

5.7 Summary of Functions Introduced in Chapter 5 246

Exercises 247

6 2D Graphics 265

Edward B. Magrab

6.1 Introduction: Graphics Management 266

6.2 Basic 2D Plotting Commands 269

6.2.1 Introduction 269

6.2.2 Changing a Graph’s Overall Appearance 281

6.2.3 Special Purpose Graphs 281

6.2.4 Reading, Displaying, and Manipulating Digital Images 288

6.3 Graph Annotation and Enhancement 290

6.3.1 Introduction 290

6.3.2 Axes and Curve Labels, Figure Titles, Legends, and Text Placement 290

6.3.3 Filling Regions 294

6.3.4 Greek Letters, Mathematical Symbols, Subscripts, and Superscripts 297

6.3.5 Altering the Attributes of Axes, Curves,Text, and Legends 300

6.3.6 Positioning One Figure Inside Another Figure 304

6.3.7 Interactive Plotting Tools 306

6.3.8 Animation 307

6.4 Examples 310

6.5 Summary of Functions Introduced in Chapter 6 319

Exercises 320

7 3D Graphics 338

Edward B. Magrab

7.1 Lines in 3D 338

7.2 Surfaces 341

7.3 Summary of Functions Introduced in Chapter 7 369

Exercises 370

8 Engineering Statistics 377

Edward B. Magrab

8.1 Descriptive Statistical Quantities 377

8.2 Probability Distributions 383

8.2.1 Discrete Distributions 383

8.2.2 Continuous Distributions 387

8.3 Confidence Intervals 397

8.4 Hypothesis Testing 401

8.5 Linear Regression 404

8.5.1 Simple Linear Regression 404

8.5.2 Multiple Linear Regression 408

8.6 Design of Experiments 415

8.6.1 Single-Factor Experiments: Analysis of Variance 415

8.6.2 Multiple-Factor Factorial Experiments 419

8.7 Summary of Functions Introduced in Chapter 8 435

Exercises 436

9 Dynamics and Vibrations 445

Balakumar Balachandran

9.1 Dynamics of Particles and Rigid Bodies 446

9.1.1 Planar Pendulum 446

9.1.2 Orbital Motions 447

9.1.3 Principal Moments of Inertia 450

9.1.4 Stability of a Rigid Body 451

9.2 Single-Degree-of-Freedom Vibratory Systems 454

9.2.1 Introduction 454

9.2.2 Linear Systems: Free Oscillations 456

9.2.3 Linear Systems: Forced Oscillations 462

9.2.4 Nonlinear Systems: Free Oscillations 469

9.2.5 Nonlinear Systems: Forced Oscillations 478

9.3 Systems with Multiple Degrees of Freedom 481

9.3.1 Two-Degree-of-Freedom Systems: Free and Forced Oscillations 481

9.3.2 Natural Frequencies and Mode Shapes 495

9.4 Free and Forced Vibrations of Euler—Bernoulli and Timoshenko Beams 499

9.4.1 Natural Frequencies and Mode Shapes of Euler—Bernoulli and Timoshenko Beams 499

9.4.2 Forced Oscillations of Euler—Bernoulli Beams 509

9.5 Summary of Functions Introduced in Chapter 9 Exercises 513

Exercises 514

10 Control Systems 524

Gregory C. Walsh

10.1 Introduction to Control System Design 525

10.1.1 Tools for Controller Design 527

10.1.2 Naming and File Conventions 528

10.2 Representation of Systems in MATLAB 528

10.2.1 State—Space Models 530

10.2.2 Transfer-Function Representation 535

10.2.3 Discrete-Time Models 538

10.2.4 Block Diagrams and SIMULINK 542

10.2.5 Conversion Between Representations 546

10.3 Response of Systems 547

10.3.1 Estimating Response from Systems 548

10.3.2 Estimating Response from Poles and Zeros 551

10.3.3 Estimating Systems from Response 558

10.4 Design Tools 560

10.4.1 Design Criteria 561

10.4.2 Design Tools 564

10.5 Design Examples 573

10.5.1 Notch Control of a Flexible Pointer 574

10.5.2 PID Control of a Magnetic Suspension System 582

10.5.3 Lead Control of an Inverted Pendulum 589

10.5.4 Control of a Magnetically Suspended Flywheel 596

10.6 Summary of Functions Introduced in Chapter 10 605

Exercises 606

11 Fluid Mechanics 614

James H. Duncan

11.1 Hydrostatics 614

11.1.1 Pressure Distribution in the Standard Atmosphere 615

11.1.2 Force on a Planar Gate 616

11.2 Internal Viscous Flow 621

11.2.1 Laminar Flow in a Horizontal Pipe with Circular Cross Section 621

11.2.2 Downward Turbulent Flow in a Vertical Pipe 622

11.2.3 Three Connected Reservoirs 624

11.3 External Flow 626

11.3.1 Boundary Layer on an Infinite Plate Started Suddenly from Rest 626

11.3.2 Blasius Boundary Layer 628

11.3.3 Potential Flow 631

11.3.4 Joukowski Airfoils 636

11.4 Open Channel Flow 641

11.5 Biological Flows 646

Exercises 648

12 Heat Transfer 659

Keith E. Herold

12.1 Conduction Heat Transfer 660

12.1.1 Transient Heat Conduction in a Semi-Infinite Slab with Surface Convection 660

12.1.2 Transient Heat Conduction in an Infinite Solid Cylinder with Convection 662

12.1.3 Transient One-Dimensional Conduction with a Heat Source 664

12.2 Convection Heat Transfer 668

12.2.1 Internal Flow Convection: Pipe Flow 668

12.2.2 Thermal Boundary Layer on a Flat Plate: Similarity Solution 672

12.2.3 Natural Convection Similarity Solution 677

12.3 Radiation Heat Transfer 682

12.3.1 Radiation View Factor: Differential Area to Arbitrary Rectangle in Parallel Planes 682

12.3.2 View Factor Between Two Rectangles in Parallel Planes 685

12.3.3 Enclosure Radiation with Diffuse Gray Walls 687

12.3.4 Transient Radiation Heating of a Plate in a Furnace 690

Exercises 692

13 Optimization 702

Shapour Azarm

13.1 Definition, Formulation, and Graphical Solution 703

13.1.1 Introduction 703

13.1.2 Graphical Solution 703

13.2 Linear Programming 706

13.3 Binary Integer Programming 709

13.4 Nonlinear Programming: Unconstrained and Curve Fitting 710

13.4.1 Unconstrained Optimization 710

13.4.2 Curve Fitting: One Independent Variable 713

13.4.3 Curve Fitting: Several Independent Variables 715

13.5 Nonlinear Programming: Constrained Single Objective 719

13.5.1 Constrained Single-Variable Method 719

13.5.2 Constrained Multivariable Method 721

13.5.3 Quadratic Programming 730

13.5.4 Semi-Infinitely Constrained Method 732

13.6 Multiobjective Optimization 736

13.7 Genetic Algorithm-Based Optimization 742

13.8 Summary of Functions Introduced in Chapter 13 751

Exercises 752

14 Biological Systems: Transport of Heat, Mass, and Electric Charge 769

Keith E. Herold

14.1 Heat Transfer in Biological Systems 770

14.1.1 Heat Transfer in Perfused Tissue 770

14.1.2 Thermal Conductivity Determination 773

14.2 Mass Transfer in Biological Systems 775

14.2.1 Bicarbonate Buffer System 775

14.2.2 Carbon Dioxide Transport in Blood 778

14.2.3 Oxygen Transport in Blood 779

14.2.4 Perfusion Bioreactor 782

14.2.5 Supply of Oxygen to a Spherical Tumor 786

14.2.6 Krogh Cylinder Model of Tissue Oxygenation 789

14.3 Charge Transport in Biological Systems 796

14.3.1 Hodgkin—Huxley Neuron Model 796

14.3.2 Hodgkin—Huxley Gating Parameters 797

14.3.3 Hodgkin—Huxley Model with Step Function Input 802

14.3.4 Action Potential 804

Exercises 807

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Engineers Guide to MATLAB

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