Cover -- Preface -- Acknowledgements -- Contents -- Chapter 1 Introduction to Mechanical Vibrations -- 1.1 Classification of Vibrations -- 1.2 Elementary Parts of Vibrating Systems -- 1.3 Periodic Motion -- 1.4 Discrete and Continuous Systems -- 1.5 Vibration Analysis -- 1.5.1 Components of Vibrating Systems -- 1.6 Free Vibration of Single Degree of Freedom Systems -- 1.6.1 Free Vibration of an Undamped Translational System -- 1.6.2 Free Vibration of an Undamped Torsional System -- 1.6.3 Energy Method -- 1.6.4 Stability of Undamped Linear Systems -- 1.6.5 Free Vibration With Viscous Damping -- 1.6.6 Logarithmic Decrement -- 1.6.7 Torsional System With Viscous Damping -- 1.6.8 Free Vibration with Coulomb Damping -- 1.6.9 Free Vibration with Hysteretic Damping -- 1.7 Forced Vibration of Single-Degree-of-Freedom Systems -- 1.7.1 Forced Vibrations of Damped System -- 1.7.1.1 Resonance -- 1.7.2 Beats -- 1.7.3 Transmissibility -- 1.7.4 Quality Factor and Bandwidth -- 1.7.5 Rotating Unbalance -- 1.7.6 Base Excitation -- 1.7.7 Response Under Coulomb Damping -- 1.7.8 Response Under Hysteresis Damping -- 1.7.9 General Forcing Conditions and Response -- 1.7.10 Fourier Series and Harmonic Analysis -- 1.8 Harmonic Functions -- 1.8.1 Even Functions -- 1.8.2 Odd Functions -- 1.8.3 Response Under a Periodic Force of Irregular Form -- 1.8.4 Response Under a General Periodic Force -- 1.8.5 Transient Vibration -- 1.8.6 Unit Impulse -- 1.8.7 Impulsive Response of a System -- 1.8.8 Response to an Arbitrary Input -- 1.8.9 Laplace Transformation Method -- 1.9 Two Degree of Freedom Systems -- 1.9.1 Equations of Motion -- 1.9.2 Free Vibration Analysis -- 1.9.3 Torsional System -- 1.9.4 Coordinate Coupling and Principal Coordinates -- 1.9.5 Forced Vibrations -- 1.9.6 Orthogonality Principle -- 1.10 Multi-Degree-of-Freedom Systems -- 1.10.1 Equations of Motion.

1.10.2 Stiffness Influence Coefficients -- 1.10.3 Flexibility Influence Coefficients -- 1.10.4 Matrix Formulation -- 1.10.5 Inertia Influence Coefficients -- 1.10.6 Normal Mode Solution -- 1.10.7 Natural Frequencies and Mode Shapes -- 1.10.8 Mode Shape Orthogonality -- 1.10.9 Response of a System to Initial Conditions -- 1.11 Free Vibration of Damped Systems -- 1.12 Proportional Damping -- 1.13 General Viscous Damping -- 1.14 Harmonic Excitations -- 1.15 Modal Analysis for Undamped Systems -- 1.16 Largange's Equation -- 1.16.1 Generalized Coordinates -- 1.17 Principle of Virtual Work -- 1.18 D'Alembert's Principle -- 1.19 Lagrange's Equations of Motion -- 1.20 Variational Principles -- 1.21 Hamilton's Principle -- References -- Glossary of Terms -- Chapter 2 MATLAB Basics -- 2.1 Introduction -- 2.1.1 Starting and Quitting MATLAB -- 2.1.2 Display Windows -- 2.1.3 Entering Commands -- 2.1.4 MATLAB Expo -- 2.1.5 Abort -- 2.1.6 The Semicolon ( -- ) -- 2.1.7 Typing % -- 2.1.8 The clc Command -- 2.1.9 Help -- 2.1.10 Statements and Variables -- 2.2 Arithmetic Operations -- 2.3 Display Formats -- 2.4 Elementary Math Built-in Functions -- 2.5 Variable Names -- 2.6 Predefined Variables -- 2.7 Commands for Managing Variables -- 2.8 General Commands -- 2.9 Arrays -- 2.9.1 Row Vector -- 2.9.2 Column Vector -- 2.9.3 Matrix -- 2.9.4 Addressing Arrays -- 2.9.4.1 Colon for a vector -- 2.9.4.2 Colon for a matrix -- 2.9.5 Adding Elements to a Vector or a Matrix -- 2.9.6 Deleting Elements -- 2.9.7 Built-In Functions -- 2.10 Operations With Arrays -- 2.10.1 Addition and Subtraction of Matrices -- 2.10.2 Dot Product -- 2.10.3 Array Multiplication -- 2.10.4 Array Division -- 2.10.5 Identity Matrix -- 2.10.6 Inverse of a Matrix -- 2.10.7 Transpose -- 2.10.8 Determinant -- 2.10.9 Array Division -- 2.10.10 Left Division -- 2.10.11 Right Division.

2.10.12 Eigenvalues and Eigenvectors -- 2.11 Element-by-element Operations -- 2.11.1 Built-in Functions for Arrays -- 2.12 Random Numbers Generation -- 2.12.1 The Random Command -- 2.13 Polynomials -- 2.14 System of Linear Equations -- 2.14.1 Matrix Division -- 2.14.2 Matrix Inverse -- 2.15 Script Files -- 2.15.1 Creating and Saving a Script File -- 2.15.2 Running a Script File -- 2.15.3 Input to a Script File -- 2.15.4 Output Commands -- 2.16 Programming in MATLAB -- 2.16.1 Relational and Logical Operators -- 2.16.2 Order of Precedence -- 2.16.3 Built-in Logical Functions -- 2.16.4 Conditional Statements -- 2.16.5 nested if Statements -- 2.16.6 else AND else if CLAUSES -- 2.16.7 MATLAB while Structures -- 2.17 Graphics -- 2.17.1 Basic 2-D Plots -- 2.17.2 Specialized 2-D Plots -- 2.17.2.1 Overlay Plots -- 2.17.3 3-D Plots -- 2.17.4 Saving and Printing Graphs -- 2.18 Input / Output in MATLAB -- 2.18.1 The fopen Statement -- 2.19 Symbolic Mathematics -- 2.19.1 Symbolic Expressions -- 2.19.2 Solution to Differential Equations -- 2.19.3 Calculus -- 2.20 The Laplace Transforms -- 2.20.1 Finding Zeros and Poles of B(s)/A(s) -- 2.21 Control Systems -- 2.21.1 Transfer Functions -- 2.21.2 Model Conversion -- 2.22 The Laplace Transforms -- 10.11.1 Finding Zeros and Poles of B(s)/A(s) -- Model Problems and Solutions -- 2.23 Summary -- References -- Problems -- Chapter 3 MATLAB Tutorial -- 3.1 Introduction -- 3.2 Example Problems and Solutions -- 3.3 Summary -- Problems -- Bibliography.

Solving Engineering Vibration Analysis Problems using MATLAB book is designed as an introductory undergraduate or graduate course for engineering students of all disciplines. Vibration analysis is a multidisciplinary subject and presents a system dynamics methodology based on mathematical fundamentals and stresses physical system modeling. The classical methods of vibration analysis engineering are covered: matrix analysis, Laplace transforms and transfer functions.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.