Fractional Random Vibrations I

Theories

Ming Li

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English

CRC Press
03 October 2025

Mechanical engineering; Materials science; Computer networking & communications; Computer architecture & logic design

Series: 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. Volume I deals succinctly with the theories of fractional processes and fractional vibration systems.

A major focus of fractional vibrations is the derivation of analytical expressions for the frequency transfer functions of seven classes of fractional vibrations using elementary functions. This is considered from the perspective of the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness. The present results serve as a basis for the study of the novel and frontier topic of fractional processes passing through fractional vibration systems, which is discussed in Volume II.

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

By: Ming Li
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
ISBN: 9781041110194
ISBN 10: 1041110197
Series: Fractional Order Thinking in Exploring the Frontiers of STEM
Pages: 158
Publication Date: 03 October 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming

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

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.