Page 14 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

ContEntS 11
3.15 Examples Using MATLAB 365 Problems 484
Chapter Summary 371 Design Projects 506
References 371
Review Questions 372
Problems 375 ChAPtEr 5
Design Projects 402 two-Degree-of-Freedom Systems 509
5.1 Introduction 510
ChAPtEr 4 5.2 Equations of Motion for Forced
Vibration 514
Vibration Under General Forcing 5.3 Free-Vibration Analysis of an Undamped
Conditions 403 System 516
4.1 Introduction 404 5.4 Torsional System 525
4.2 Response Under a General 5.5 Coordinate Coupling and Principal
Periodic Force 405 Coordinates 530
4.2.1 First-Order Systems 406 5.6 Forced-Vibration Analysis 536
4.2.2 Second-Order Systems 412 5.7 Semidefinite Systems 539
4.3 Response Under a Periodic Force 5.8 Self-Excitation and Stability Analysis 542
of Irregular Form 418 5.9 Transfer-Function Approach 544
4.4 Response Under a Nonperiodic Force 420 5.10 Solutions Using Laplace Transform 546
4.5 Convolution Integral 421 5.11 Solutions Using Frequency Transfer
4.5.1 Response to an Impulse 422 Functions 554
4.5.2 Response to a General Forcing 5.12 Examples Using MATLAB 557
Condition 425 Chapter Summary 564
4.5.3 Response to Base Excitation 426 References 565
4.6 Response Spectrum 434 Review Questions 565
4.6.1 Response Spectrum for Base Problems 568
Excitation 436 Design Projects 594
4.6.2 Earthquake Response Spectra 439
4.6.3 Design Under a Shock Environment 443 ChAPtEr 6
4.7 Laplace Transforms 446
4.7.1 Transient and Steady-State Multidegree-of-Freedom Systems 596
Responses 446 6.1 Introduction 598
4.7.2 Response of First-Order Systems 447 6.2 Modeling of Continuous Systems as Multidegree-
4.7.3 Response of Second-Order of-Freedom Systems 598
Systems 449 6.3 Using Newton’s Second Law to Derive Equations
4.7.4 Response to Step Force 454 of Motion 600
4.7.5 Analysis of the Step Response 460 6.4 Influence Coefficients 605
4.7.6 Description of Transient Response 461 6.4.1 Stiffness Influence Coefficients 605
4.8 Numerical Methods 467 6.4.2 Flexibility Influence Coefficients 610
4.8.1 Runge-Kutta Methods 469 6.4.3 Inertia Influence Coefficients 615
4.9 Response to Irregular Forcing Conditions Using 6.5 Potential and Kinetic Energy Expressions in
Numerical Methods 471 Matrix Form 617
4.10 Examples Using MATLAB 476 6.6 Generalized Coordinates and Generalized
Chapter Summary 480 Forces 619
References 480 6.7 Using Lagrange’s Equations to Derive Equations
Review Questions 481 of Motion 620