Fractional Random Vibrations II: Applications

by Ming Li

Overview

This two-volume set provides a comprehensive study of fractional random vibration from the perspective of theory and practice. Volume II provides the analytical expressions for the responses of seven classes of fractional vibration systems excited by six types of random processes.

It examines the responses of seven classes of fractional vibrations driven by five fractional processes, namely, fractional Gaussian noise, generalized fractional Gaussian noise, fractional Brownian motion, fractional Ornstein-Uhlenbeck process, the process with the von Kármán spectrum, and the process with the Pierson-Moskowitz spectrum. The present results apply the theories discussed in Volume I to the novel and cutting-edge topic of fractional processes, with a special focus on fractional vibration systems for marine structures influenced by the Pierson-Moskowitz and von Kármán spectra.

The title will be essential reading for students, mathematicians, physicists, and engineers interested in fractional random vibration phenomena.

Product Details

ISBN-13:	9781040430750
Publisher:	CRC Press
Publication date:	10/29/2025
Series:	Fractional Order Thinking in Exploring the Frontiers of STEM
Sold by:	Barnes & Noble
Format:	eBook
Pages:	160

About the Author

Ming Li is a professor at Ocean College, Zhejiang University, China, and an emeritus professor at East China Normal University. He has been a contributor for many years to the fields of mathematics, statistics, mechanics, and computer science. His publications with CRC Press also include Multi-Fractal Traffic and Anomaly Detection in Computer Communications, Fractal Teletraffic Modeling and Delay Bounds in Computer Communications, and Fractional Vibrations with Applications to Euler-Bernoulli Beams.

Table of Contents

1 Responses of Fractional Vibrations Driven by Pierson-Moskowitz Spectrum 2 Responses of Fractional Vibrations Driven by Fractional Gaussian Noise 3 Responses of Fractional Vibrations Driven by Generalized Fractional Gaussian Noise 4 Responses of Fractional Vibrations Driven by Fractional Brownian Motion 5 Responses of Fractional Vibrations Driven by Fractional Ornstein-Uhlenbeck Proces 6 Responses of Fractional Vibrations Driven by von Kármán Spectrum 7 Postscript to Volume II