Fractional Vibrations with Applications to Euler-Bernoulli Beams

ISBN-13: 9781032603605 / Twarda / 2023 / 528 str.

Ming Li

Opis

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.

Spis treści

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

O autorze

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.