Fractional Vibrations with Applications to Euler-Bernoulli Beams

<p>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.</p><p>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.</p><p>This title will be a must-read for students mathematicians physicists and engineers interested in vibration phenomena and novel vibration performances especially fractional vibrations.</p>