Vibration of Discrete and Continuous Systems

This revised, updated textbook adds new focus on computational methods and the importance of vibration theory in computer-aided engineering to fundamental aspects of vibration of discrete and continuous systems covered in the previous two editions of Vibration of Discrete and Continuous Systems. Building on the book's emphasis on the theory of vibration of mechanical, structural, and aerospace systems, the author's modifications, including discussion of the sub-structuring and finite element formulations, complete the coverage of topics required for a contemporary, second course following Vibration Theory. The textbook is appropriate for both upper-level undergraduate and graduate courses.

• Expands coverage by more than 200 pages over the previous edition;
• Grounds detail of vibration within discrete and continuous systems with thorough references to the theory of vibration;
• Explains coverage of computational methods in the vibration analysis;
• Illustrates the use of the finite element method and sub-structuring techniques in the vibration analysis;
• Reinforces concepts with over 200 end-of-chapter problems;

• Facilitates readers' digestion of critical concepts using matrix methods to present some advanced vibration topics in a tractable manner.

Auteur

Ahmed Shabana, is UIC Distinguished Professor and Richard and Loan Hill Professor of Engineering at the Univ of Illinois Chicago.

Contenu

1 Introduction.- 1.1 Kinematics of Rigid Bodies.- 1.2 Dynamic Equations.- 1.3 Single Degree of Freedom Systems.- 1.4 Oscillatory and Nonoscillatory Motion.- 1.5 Other Types of Damping.- 1.6 Forced Vibration.- 1.7 Impulse Response.- 1.8 Response to an Arbitrary Forcing Function.- Problems.- 2 Lagrangian Dynamics.- 2.1 Generalized Coordinates.- 2.2 Virtual Work and Generalized Forces.- 2.3 Lagrange's Equation.- 2.4 Kinetic Energy.- 2.5 Strain Energy.- 2.6 Hamilton's Principle.- 2.7 Conservation Theorems.- 2.8 Concluding Remarks.- Problems.- 3 Multi-Degree of Freedom Systems.- 3.1 Equations of Motion.- 3.2 Undamped Free Vibration.- 3.3 Orthogonality of the Mode Shapes.- 3.4 Rigid-Body Modes.- 3.5 Conservation of Energy.- 3.6 Forced Vibration of the Undamped Systems.- 3.7 Viscously Damped Systems.- 3.8 General Viscous Damping.- 3.9 Approximation and Numerical Methods.- 3.10 Matrix-Iteration Methods.- 3.11 Method of Transfer Matrices173 Problems.- 4 Vibration of Continuous Systems.- 4.1 Free Longitudinal Vibrations.- 4.2 Free Torsional Vibrations.- 4.3 Free Transverse Vibrations of Beams.- 4.4 Orthogonality of the Eigenfunctions.- 4.5 Forced Vibrations.- 4.6 Inhomogeneous Boundary Conditions.- 4.7 Viscoelastic Materials.- 4.8 Energy Methods.- 4.9 Approximation Methods.- 4.10 Galerkin's Method.- 4.11 Assumed-Modes Method259 Problems.- 5 The Finite-Element Method.- 5.1 Assumed Displacement Field.- 5.2 Comments on the Element Shape Functions.- 5.3 Connectivity Between Elements.- 5.4 Formulation of the Mass Matrix.- 5.5 Formulation of the Stiffness Matrix.- 5.6 Equations of Motion.- 5.7 Convergence of the Finite-Element Solution.- 5.8 Higher-Order Elements.- 5.9 Spatial Elements.- 5.10 Large Rotations and Deformations323 Problems.- 6 Methods for the Eigenvalue Analysis.- 6.1 Similarity Transformation.- 6.2 Polynomial Matrices.- 6.3 Equivalence of the Characteristic Matrices.- 6.4 Jordan Matrices.- 6.5 Elementary Divisors.- 6.6 Generalized Eigenvectors.- 6.7 Jacobi Method.- 6.8 Householder Transformation.- Appendix A Linear Algebra.- A.1 Matrices.- A.2 Matrix Operations.- A.3 Vectors.- A.4 Eigenvalue Problem.- Problems.- References.