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

  • Book
  • © 2020

Overview

Authors:
  1. Isaac Elishakoff

    1. Boca Raton, USA

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  • Clarifies the common misconception that natural frequencies of structures are well apart from each other

  • Illustrates that the interaction of associated modes in plates can dramatically alter the random response due to presence of coinciding frequencies

  • Demonstrates that natural frequencies in beams on elastic foundation, as well as cylindrical or spherical shells, might cluster together resulting in substantial percentage error if cross-correlations are ignored?

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. Normal-Mode Approach in Random Vibrations

    • Isaac Elishakoff
    Pages 1-35

  3. Random Vibration of System with Finitely Many Degrees of Freedom and Several Coalescent Natural Frequencies

    • Isaac Elishakoff
    Pages 37-49

  4. Random Vibration of a Vehicle Model

    • Isaac Elishakoff
    Pages 51-62

  5. Hybrid Optimization and Anti-optimization of a Stochastically Excited Beam

    • Isaac Elishakoff
    Pages 63-90

  6. Random Vibration of a Point-Driven Two-Span Beam on an Elastic Foundation

    • Isaac Elishakoff
    Pages 91-125

  7. Random Vibrations of Orthotropic Plates

    • Isaac Elishakoff
    Pages 127-140

  8. Wide-Band Random Axisymmetric Vibration of Cylindrical Shells

    • Isaac Elishakoff
    Pages 141-154

  9. Turbulent Flow-Excited Vibrations of a Shallow Cylindrical Shell

    • Isaac Elishakoff
    Pages 155-179

  10. On the Role of Cross-Correlations in the Random Vibrations of Spherical Shells

    • Isaac Elishakoff
    Pages 181-200

  11. Dramatic Effect of Cross-Correlations in Random Vibration of Point-Driven Flat Plate and Spherically Curved Panel

    • Isaac Elishakoff
    Pages 201-220

  12. Back Matter

    Pages 221-338
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Keywords

About this book

This volume explains the dramatic effect of cross-correlations in forming the structural response of aircraft in turbulent excitation, ships in rough seas, cars on irregular roads, and other dynamic regimes. It brings into sharp focus the dramatic effect of cross correlations often neglected due to the analytical difficulty of their evaluation. Veteran author Professor Isaac Elishakoff illustrates how neglect of cross correlations could result in underestimation of the response by tens or hundreds of percentages the effect of the random vibrations of structures’ main elements, including beams, plates, and shells.

Authors and Affiliations

  • Boca Raton, USA

    Isaac Elishakoff

About the author

Professor ​Isaac Elishakoff is Distinguished Research Professor in the Ocean and Mechanical Engineering Department in the Florida Atlantic University, Boca Raton, Florida. He is an authoritative figure in the broad area of mechanics and has made several contributions in the areas of random vibrations, solid mechanics of composite material, semi-inverse problems of vibrations and stability, functionally graded material structures and nanotechnology. Dr. Elishakoff has nearly 500 articles in the journal literature,30 authored, co-authored, edited or co-edited books, and over 200 national and international talks at conferences and seminars.

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