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E-grāmata: Fractional Vibrations with Applications to Euler-Bernoulli Beams

  • Formāts: 558 pages
  • Izdošanas datums: 29-Dec-2023
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781003801146
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Fractional Vibrations with Applications to Euler-Bernoulli BeamsPalielināt
  • Formāts: 558 pages
  • Izdošanas datums: 29-Dec-2023
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781003801146
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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.



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.

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 Kįrmįn Spectrum from a View of Fractal
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.
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