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li m fractional vibrations applications euler bernoulli beams 2024

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Textbook in PDF format This 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 ship 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, depending 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 and physicists, and engineers interested in vibration phenomena and novel vibration performances, especially fractional vibrations. Preface. Acknowledgments. Fundamentals. Harmonic Vibrations. Vibrations Excited by Periodic Forces. Fourier Transform and Spectra. Responses Excited by Deterministically Aperiodic Forces. Vibrations with Multiple Degrees-of-Freedom. Vibrations of Distributed Systems and Euler-Bernoulli Beam. Fractional Vibrations. Six Classes of Fractional Vibrations. Fractional Vibrations of Class I. Fractional Vibrations of Class II. Class III Fractional Vibrations. Fractional Vibrations of Class IV. Class V Fractional Vibrations. Fractional Vibrations of Class VI. Explanation of Rayleigh Damping Assumption Based on Fractional Vibrations. Mass. Vibrators with Variable-Order Fractional Forces. Fractional Euler-Bernoulli Beams. Free Response to Longitudinal Vibrations of Uniform Circular Beam with Fractional Coordinates. Free Response to Euler-Bernoulli Beam with Fractional Coordinates. Forced Response to Euler-Bernoulli Beam with Fractional Coordinates. Seven Classes of Fractionally Damped Euler-Bernoulli Beams. Forced Response to Damped Euler-Bernoulli Beam with Fractional Inertia Force (Class 1). Forced Response to Damped Euler-Bernoulli Beam with Fractional External Damping Force (Class 2). Forced Response to Damped Euler-Bernoulli Beam with Fractional Internal Damping Force (Class 3). Forced Response to Damped Euler-Bernoulli Beam with Fractional External and Internal Damping Forces (Class 4). Forced Response to Damped Euler-Bernoulli Beam with Fractional Inertia and External Damping Forces (Class 5). Forced Response to Damped Euler-Bernoulli Beam with Fractional Inertia and Internal Damping Forces (Class 6). Forced Response to Multi-Fractional Damped Euler-Bernoulli Beam (Class 7). Notes on Fractional Vibrations. Some Techniques in Vibrations. Sampling, Aliasing, Anti-Aliasing Filtering and Time Signal Leakage. A Method for Requiring Block Size for Spectrum Measurement of Ocean Surface Waves. Time-Frequency Distributions of Encountered Waves Using Hilbert-Huang Transform. An Optimal Controller of an Irregular Wave Maker. On von Kármán Spectrum from a View of Fractal. Index

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li m fractional vibrations applications euler bernoulli beams 2024

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