## ABSTRACT

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|161 pages

Fundamentals

part II|192 pages

Fractional Vibrations

part III|113 pages

Fractional Euler-Bernoulli Beams

chapter Chapter 17|18 pages

#### Free Response to Longitudinal Vibrations of Uniform Circular Beam with Fractional Coordinates

chapter Chapter 21|9 pages

#### Forced Response to Damped Euler-Bernoulli Beam with Fractional Inertia Force (Class 1)

chapter Chapter 22|8 pages

#### Forced Response to Damped Euler-Bernoulli Beam with Fractional External Damping Force (Class 2)

chapter Chapter 23|8 pages

#### Forced Response to Damped Euler-Bernoulli Beam with Fractional Internal Damping Force (Class 3)

chapter Chapter 27|10 pages

#### Forced Response to Multi-Fractional Damped Euler-Bernoulli Beam (Class 7)

part IV|57 pages

Some Techniques in Vibrations