Fractional Random Vibrations

Two Volume Set
1. Auflage 2025
ISBN: 978-1-041-11174-0
Verlag: Taylor & Francis Ltd

Buch, Englisch, 280 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Fractional Order Thinking in Exploring the Frontiers of STEM

This two-volume set provides a comprehensive study of fractional random vibration from the perspective of theory and practice. By fractional random vibration, we mean the random vibration of fractional vibration systems driven by fractional processes.

Volume I explores the fundamentals of fractional processes and fractional vibration systems. A major focus is the derivation of analytical expressions for the frequency transfer functions of seven classes of fractional vibrations using elementary functions. Theoretical support is provided by the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness. Volume II provides the analytical expressions for the responses of seven classes of fractional vibration systems subjected to fractional Gaussian noise, generalized fractional Gaussian noise, fractional Brownian motion, the fractional Ornstein-Uhlenbeck process, the process with the von Kármán spectrum, and the one with the Pierson-Moskowitz spectrum. It applies the theories discussed in Volume I to the novel and cutting-edge topic of fractional processes, with special emphasis on fractional vibration systems for marine structures influenced by the Pierson-Moskowitz and von Kármán spectra.

The titles will be essential reading for students, mathematicians, physicists, and engineers interested in vibration phenomena driven by fractional processes.

Zielgruppe

Postgraduate and Professional Reference

Autoren/Hrsg.

Li, Ming

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Technische Wissenschaften Verkehrstechnik | Transportgewerbe Meerestechnik, ablandige Plattformen
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

Vol I: 1 Fundamentals of Harmonic Vibrations 2 Random Processes 3 Fractional Processes 4 Responses of Random Vibration Systems and Input-Output Relations 5 Vibrations with Frequency Dependent Mass, Damping, and Stiffness 6 Classification of Fractional Vibrations 7 Seven Classes of Fractional Vibrations 8 Postscript to Volume I

Vol II: 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

Über Autor(innen)

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.