Fractional Vibrations with Applications to Euler-Bernoulli Beams

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 Karman Spectrum from a View of Fractal