Vibration of continuous systems /
Singiresu S Rao, University of Miami.
- Second edition.
- 1 online resource
Includes bibliographical references and index.
Cover; Title Page; Copyright; Contents; Preface; Acknowledgments; About the Author; Chapter 1 Introduction: Basic Concepts and Terminology; 1.1 Concept of Vibration; 1.2 Importance of Vibration; 1.3 Origins and Developments in Mechanics and Vibration; 1.4 History of Vibration of Continuous Systems; 1.5 Discrete and Continuous Systems; 1.6 Vibration Problems; 1.7 Vibration Analysis; 1.8 Excitations; 1.9 Harmonic Functions; 1.9.1 Representation of Harmonic Motion; 1.9.2 Definitions and Terminology; 1.10 Periodic Functions and Fourier Series; 1.11 Nonperiodic Functions and Fourier Integrals 1.12 Literature on Vibration of Continuous SystemsReferences; Problems; Chapter 2 Vibration of Discrete Systems: Brief Review; 2.1 Vibration of a Single-Degree-of-Freedom System; 2.1.1 Free Vibration; 2.1.2 Forced Vibration under Harmonic Force; 2.1.3 Forced Vibration under General Force; 2.2 Vibration of Multidegree-of-Freedom Systems; 2.2.1 Eigenvalue Problem; 2.2.2 Orthogonality of Modal Vectors; 2.2.3 Free Vibration Analysis of an Undamped System Using Modal Analysis; 2.2.4 Forced Vibration Analysis of an Undamped System Using Modal Analysis 2.2.5 Forced Vibration Analysis of a System with Proportional Damping2.2.6 Forced Vibration Analysis of a System with General Viscous Damping; 2.3 Recent Contributions; References; Problems; Chapter 3 Derivation of Equations: Equilibrium Approach; 3.1 Introduction; 3.2 Newton's Second Law of Motion; 3.3 D'Alembert's Principle; 3.4 Equation of Motion of a Bar in Axial Vibration; 3.5 Equation of Motion of a Beam in Transverse Vibration; 3.6 Equation of Motion of a Plate in Transverse Vibration; 3.6.1 State of Stress; 3.6.2 Dynamic Equilibrium Equations; 3.6.3 Strain-Displacement Relations 3.6.4 Moment-Displacement Relations3.6.5 Equation of Motion in Terms of Displacement; 3.6.6 Initial and Boundary Conditions; 3.7 Additional Contributions; References; Problems; Chapter 4 Derivation of Equations: Variational Approach; 4.1 Introduction; 4.2 Calculus of a Single Variable; 4.3 Calculus of Variations; 4.4 Variation Operator; 4.5 Functional with Higher-Order Derivatives; 4.6 Functional with Several Dependent Variables; 4.7 Functional with Several Independent Variables; 4.8 Extremization of a Functional with Constraints; 4.9 Boundary Conditions 4.10 Variational Methods in Solid Mechanics4.10.1 Principle of Minimum Potential Energy; 4.10.2 Principle of Minimum Complementary Energy; 4.10.3 Principle of Stationary Reissner Energy; 4.10.4 Hamilton's Principle; 4.11 Applications of Hamilton's Principle; 4.11.1 Equation of Motion for Torsional Vibration of a Shaft (Free Vibration); 4.11.2 Transverse Vibration of a Thin Beam; 4.12 Recent Contributions; Notes; References; Problems; Chapter 5 Derivation of Equations: Integral Equation Approach; 5.1 Introduction; 5.2 Classification of Integral Equations