Dynamics of Rods (eBook)

Valery A. Svetlitsky (Autor)

eBook Download: PDF

2005 | 2005
XII, 448 Seiten
Springer Berlin (Verlag)
978-3-540-26490-3 (ISBN)

Infos

This is the first and only monograph on this subject, and provides a systematic presentation of theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Includes problems and solutions for self-study.

Inhalt

Preface 5
Table of Contents 6
Introduction 12
1. Kinematics 20
1.1 Basic Relationships 20
1.2 Kinematic Equations 30
2. General Equations of Motion 36
2.1 Nonlinear Equations of Motion 36
2.2 Equations of Motion of a Rod Relative to Equilibrium Configuration 53
2.3 Equations of Motion of a Rod with Concentrated Masses 55
2.4 Equations of Stationary Motion of a Rod 57
3. Small Vibrations of Space-Curved Rods 68
3.1 Equations of Small Vibrations 70
3.2 Equations of Small Vibrations of a Rod About its Natural Configuration 80
3.3 Equations of Small Vibrations of a Rotating Rod 86
3.4 Small Vibrations About a Stationary Motion 89
3.5 Problems 94
4. Determination of Eigenvalues and Eigenfunctions 98
4.1 Determination of Eigenvalues (Eigenfrequences) in Conservative Problems 99
4.2 Determination of Eigenvalues in Nonconservative Problems 126
4.3 Eigenfunctions (Eigenvectors) 131
4.4 Approximate Methods for Determination of Eigenvalues 137
5. Free and Forced Small Vibrations 152
5.1 Free Vibrations 152
5.2 Exact Numerical Solution 155
5.3 Approximate Solution of the Equations of Small Vibrations 158
5.4 Small Vibrations of a Rod Due to an Impulsive Loading 161
5.6 Steady-state Vibrations of a Rod Under Kinematic Excitation 171
5.7 Unsteady Forced Vibrations 179
5.8 Problems 179
6. Random Vibrations 182
6.1 Equations of Small Random Vibrations of Rods 184
6.2 Basic Notions of the Statistical Dynamics 186
6.3 Stationary Random Vibrations 194
6.4 Nonstationary Random Vibrations 204
7. Straight Rods 210
7.1 Equations of Small Vibrations 210
7.2 Determination of Frequencies and Vibration Modes 227
7.3 Small Vibrations About a Stationary Motion 243
7.4 Free Vibrations of a Rotating Rod 251
7.6 Random Vibrations 273
7.7 Parametric Vibrations 276
7.8 Stability of Straight Rods Loaded by Follower Forces 291
7.9 Problems 313
8. Dynamics of Rods Interacting with Airflow or Liquid Flow 318
8.1 Aerodynamic Forces on a Rod Moving in a Flow 322
8.2 Aerodynamic Forces on a Rod of Circular Cross Section Under Small Oscillations 337
8.3 Aerodynamic Forces Due to Small Oscillations for a Rod of Non-Circular Symmetrical Cross Section 340
8.4 Equations of Small Oscillations of a Rod in an Airflow or Liquid Flow 349
8.5 Nonstationary Vibrations of "Rigid" Wires of Power Lines under Action of Aerodynamic Forces 359
9. Rods Exerted by an Internal Flow of Liquid 400
9.1 Nonlinear Equations of Motion for a Space-Curved Pipeline 401
9.2 Small Vibrations of a Space-Curved Pipeline 405
9.3 Determination of Eigenvalues 410
9.4 Parametric Vibrations of a Pipeline 416
A. Elements of Some Matrixes 422
A.I Elements of the Matrixes N(1) and N(2) 422
A.2 Elements of the Matrixes P(1) and P(2) 424
A.3 Elements of the Matrixes M(1) and M(2) 426
B. Solution of the Problems 428
B.I To Chapter 3 428
B.2 To Chapter 5 433
B.3 To Chapter 7 439
Index 458

Produkt-Details

• Erscheint lt. Verlag: 6.10.2005
• Reihe/Serie: Foundations of Engineering Mechanics
• Übersetzer: E. Evseev, K. Ramodanova
• Zusatzinfo: XII, 448 p. 189 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Fahrzeugbau / Schiffbau
• Schlagworte: Determination of Eigenvalues and Eigenfunctions • Dynamics of Rods • fluid- and aerodynamics • Kinematics • Mechanics • Numerical Methods • Straight Rods • Vibration • Vibrations of Space-Curved Rods
• ISBN-10: 3-540-26490-6 / 3540264906
• ISBN-13: 978-3-540-26490-3 / 9783540264903