Page 15 - MATLAB an introduction with applications

xiv ——— Contents

7.9 Analysis of Beams 395
7.10 Friction 395
7.11 First Moments and Centroids 396
7.12 Virtual Work 397
7.13 Kinematics of a Particle 398
7.14 D’Alembert’s Principle 402
7.15 Kinematics of a Rigid Body in Plane Motion 402
7.16 Moments of Inertia 404
7.17 Dynamics of a Rigid Body in Plane Motion 406
7.18 Work and Energy 408
7.19 Impulse and Momentum 409
7.20 Three-dimensional Mechanics 411
7.21 Example Problems and Solutions 413
References 526
Problems 527

8. MECHANICAL VIBRATIONS 549–645
8.1 Introduction 549
8.2 Classification of Vibrations 549
8.3 Elementary Parts of Vibrating Systems 550
8.4 Discrete and Continuous Systems 552
8.5 Vibration Analysis 552
8.6 Components of Vibrating Systems 554
8.7 Free Vibration of Single Degree of Freedom Systems 556
8.8 Forced Vibration of Single-degree of Freedom Systems 563
8.9 Harmonic Functions 571
8.10 Two-degrees of Freedom Systems 573
8.11 Multi-degree of Freedom Systems 577
8.12 Free Vibration of Damped Systems 581
8.13 Proportional Damping 581
8.14 General Viscous Damping 582
8.15 Harmonic Excitations 582
8.16 Modal Analysis for Undamped Systems 583
8.17 Lagrange’s Equation 583
8.18 Principle of Virtual Work 584
8.19 D’Alembert’s Principle 585
8.20 Lagrange’s Equations of Motion 585
8.21 Variational Principles 585
8.22 Hamilton’s Principle 585
8.23 Example Problems and Solutions 586
References 634
Problems 638

Bibliography 647–648
Index 649–665