Ming Li

Fractional Vibrations with Applications to Euler-Bernoulli Beams (eBook, ePUB)

• Format: ePub

Produktbeschreibung

The book examines vibration phenomena with an emphasis on fractional vibrations using the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness, covering the theoretical analysis potentially applicable to structures and, in particular, ship hulls.

Covering the six classes of fractional vibrators and seven classes of fractionally damped Euler-Bernoulli beams that play a major role in hull vibrations, this book presents analytical formulas of all results with concise expressions and elementary functions that set it apart from other recondite studies. The results show that equivalent mass or damping can be negative and depends on fractional orders. Other key highlights of the book include a concise mathematical explanation of the Rayleigh damping assumption, a novel description of the nonlinearity of fractional vibrations, and a new concept of fractional motion, offering exciting additions to the field of fractional vibrations.

This title will be a must-read for students, mathematicians, physicists, and engineers interested in vibration phenomena and novel vibration performances, especially fractional vibrations.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 558
• Erscheinungstermin: 29. Dezember 2023
• Englisch
• ISBN-13: 9781003802549
• Artikelnr.: 69536329

Autorenporträt

Ming Li is a professor at Ocean College, Zhejiang University, China, and an emeritus professor at East China Normal University. He has been a contributor for many years to the fields of mathematics, statistics, mechanics, and computer science. His publications with CRC Press also include Multi-Fractal Traffic and Anomaly Detection in Computer Communications and Fractal Teletraffic Modeling and Delay Bounds in Computer Communications.

Inhaltsangabe

Part I: Fundamentals 1. Harmonic Vibrations 2. Vibrations Excited by
Periodic Forces 3. Fourier Transform and Spectra 4. Responses Excited by
Deterministically Aperiodic Forces 5. Vibrations with Multiple
Degrees-of-Freedom 6. Vibrations of Distributed Systems and Euler-Bernoulli
Beam Part II: Fractional Vibrations 7. Six Classes of Fractional Vibrations
8. Fractional Vibrations of Class I 9. Fractional Vibrations of Class II
10. Class III Fractional Vibrations 11. Fractional Vibrations of Class IV
12. Class V Fractional Vibrations 13. Fractional Vibrations of Class VI 14.
Explanation of Rayleigh Damping Assumption based on Fractional Vibrations
15. Mass 16. Vibrators with Variable-Order Fractional Forces Part III:
Fractional Euler-Bernoulli Beams 17. Free Response to Longitudinal
Vibrations of Uniform Circular Beam with Fractional Coordinates 18. Free
Response to Euler-Bernoulli Beam with Fractional Coordinates 19. Forced
Response to Euler-Bernoulli Beam with Fractional Coordinates 20. Seven
Classes of Fractionally Damped Euler-Bernoulli Beams 21. Forced Response to
Damped Euler-Bernoulli Beam with Fractional Inertia Force (Class 1) 22.
Forced Response to Damped Euler-Bernoulli Beam with Fractional External
Damping Force (Class 2) 23. Forced Response to Damped Euler-Bernoulli Beam
with Fractional Internal Damping Force (Class 3) 24. Forced Response to
Damped Euler-Bernoulli Beam with Fractional External and Internal Damping
Forces (Class 4) 25. Forced Response to Damped Euler-Bernoulli Beam with
Fractional Inertia and External Damping Forces (Class 5) 26. Forced
Response to Damped Euler-Bernoulli Beam with fractional Inertia and
Internal Damping Forces (Class 6) 27. Forced Response to Multi-Fractional
Damped Euler-Bernoulli Beam (Class 7) 28. Notes on Fractional Vibrations
Part IV: Some Techniques in Vibrations 29. Sampling, Aliasing,
Anti-Aliasing Filtering and Time Signal Leakage 30. A Method for Requiring
Block Size for Spectrum Measurement of Ocean Surface Waves 31.
Time-Frequency Distributions of Encountered Waves using Hilbert-Huang
Transform 32. An Optimal Controller of an Irregular Wave Maker 33. On von
Kármán Spectrum from a View of Fractal