Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells

Preface
	References
Contents
1 Normal-Mode Approach in Random Vibrations
	1.1 Introductory Comments
	1.2 Analysis of a Two-Degree-of-Freedom System with Coinciding Natural Frequencies
	1.3 Simple Model Illustrating Crandall’s Random Vibration Results
	1.4 Theoretical Analysis
	1.5 One Particular Case:  f2 = f3 = 0  with Probability One
	1.6 f1(t) = f3(t) = 0 with Probability One
	References
2 Random Vibration of System with Finitely Many Degrees of Freedom and Several Coalescent Natural Frequencies
	2.1 Introductory Comments
	2.2 Analysis of a Multi-Degree-of-Freedom System with Many Coinciding Frequencies
	2.3 System with Two Degrees of Freedom
	2.4 Systems with Three and More Degrees of Freedom
	References
3 Random Vibration of a Vehicle Model
	3.1 Introductory Comments
	3.2 Analysis of the Friswell Model
	3.3 Kim and Yoon’s Four-Wheel Vehicle Model
	3.4 Conclusion
	References
4 Hybrid Optimization and Anti-optimization of a Stochastically Excited Beam
	4.1 Introductory Comments
	4.2 Basic Equations
	4.3 Evaluation of the Mode Shapes
	4.4 Anti-symmetric Mode Shapes
	4.5 Limiting Cases
	4.6 Random Vibrations
	4.7 Symmetric Excitation
	4.8 Anti-symmetric Excitation
	4.9 General Case: Non-symmetric Random Excitation
	4.10 Point-Driven Excitation
	4.11 Conclusion
	References
5 Random Vibration of a Point-Driven Two-Span Beam on an Elastic Foundation
	5.1 Introductory Comments
	5.2 Random Vibrations of a Two-Span Beam Without Elastic Foundation
	5.3 Formulation of the Problem
	5.4 Natural Frequencies and Modes of the Two-Span Beam
	5.5 Random Vibration Response
	5.6 Numerical Results and Discussion
	5.7 Conclusion
	References
6 Random Vibrations of Orthotropic Plates
	6.1 Introductory Comments
	6.2 Analytical Formulation
	6.3 Random Vibrations of Plates with Opposite Edges Simply Supported
	6.4 Conclusion
	References
7 Wide-Band Random Axisymmetric Vibration of Cylindrical Shells
	7.1 Introductory Comments
	7.2 Random Vibration of a Thin Cylindrical Shell
	7.3 Description of the Calculations
	7.4 Discussion of the Results
	References
8 Turbulent Flow-Excited Vibrations of a Shallow Cylindrical Shell
	8.1 Introductory Comments
	8.2 Analytical Formulation
	8.3 Excitation Cross-Spectral Densities
	8.4 Shell Response Characteristics
	8.5 Random Vibrations in Cylindrical Shells Containing an Acoustic Medium
	8.6 Conclusion
	References
9 On the Role of Cross-Correlations in the Random Vibrations of Spherical Shells
	9.1 Introductory Comments
	9.2 Response Cross-Spectral Densities of a Spherical Shell
	9.3 Hysteretic Damping
	9.4 Example Problem and Discussion
	9.5 Conclusion
	References
10 Dramatic Effect of Cross-Correlations in Random Vibration of Point-Driven Flat Plate and Spherically Curved Panel
	10.1 Introductory Comments
	10.2 Random Vibration of a Curved Spherical Panel
	10.3 Numerical Examples and Discussion
	10.4 Conclusion
	References
Appendix  The Effect of the Eigenvectors Associated with the Repeated Frequencies
References
Bibliography
Author Index
Subject Index