Short description:

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.

Long description:

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.

Table of Contents:

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