Page 17 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

14 ContEntS
10.9.4 Vibration Monitoring Techniques 972 12.3.1 Bar Element 1045
10.9.5 Instrumentation Systems 978 12.3.2 Torsion Element 1048
10.9.6 Choice of Monitoring Parameter 978 12.3.3 Beam Element 1049
10.10 Examples Using MATLAB 979 12.4 Transformation of Element Matrices
Chapter Summary 982 and Vectors 1052
References 982 12.5 Equations of Motion of the Complete System
Review Questions 984 of Finite Elements 1055
Problems 986 12.6 Incorporation of Boundary Conditions 1057
Design Projects 992 12.7 Consistent- and Lumped-Mass Matrices 1066
12.7.1 Lumped-Mass Matrix for a Bar
Element 1066
ChAPtEr 11 12.7.2 Lumped-Mass Matrix for a Beam
numerical Integration Methods in Element 1066
Vibration Analysis 993 12.7.3 Lumped-Mass Versus Consistent-Mass
Matrices 1067
11.1 Introduction 994
11.2 Finite Difference Method 995 12.8 Examples Using MATLAB 1069
11.3 Central Difference Method for Single-Degree-of- Chapter Summary 1073
Freedom Systems 996 References 1073
11.4 Runge-Kutta Method for Single-Degree-of- Review Questions 1074
Freedom Systems 999 Problems 1076
11.5 Central Difference Method for Multidegree-of- Design Projects 1088
Freedom Systems 1001 Chapters 13 and 14 are provided as downloadable
11.6 Finite Difference Method for Continuous files on the Companion Website.
Systems 1005
11.6.1 Longitudinal Vibration of Bars 1005 ChAPtEr 13
11.6.2 Transverse Vibration of Beams 1009
11.7 Runge-Kutta Method for Multidegree-of- nonlinear Vibration 13-1
Freedom Systems 1014 13.1 Introduction 13-2
11.8 Houbolt Method 1016 13.2 Examples of Nonlinear Vibration Problems 13-3
11.9 Wilson Method 1019 13.2.1 Simple Pendulum 13-3
11.10 Newmark Method 1022 13.2.2 Mechanical Chatter, Belt Friction
11.11 Examples Using MATLAB 1026 System 13-5
Chapter Summary 1032 13.2.3 Variable Mass System 13-5
References 1032 13.3 Exact Methods 13-6
Review Questions 1033 13.4 Approximate Analytical Methods 13-7
Problems 1035 13.4.1 Basic Philosophy 13-8
13.4.2 Lindstedt’s Perturbation
Method 13-10
ChAPtEr 12 13.4.3 Iterative Method 13-13
Finite Element Method 1041 13.4.4 Ritz-Galerkin Method 13-17
12.1 Introduction 1042 13.5 Subharmonic and Superharmonic
12.2 Equations of Motion of an Element 1043 Oscillations 13-19
12.3 Mass Matrix, Stiffness Matrix, and Force 13.5.1 Subharmonic Oscillations 13-20
Vector 1045 13.5.2 Superharmonic Oscillations 13-23