preprints.org > engineering > mechanical engineering > doi: 10.20944/preprints202403.0002.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 29 February 2024 / Approved: 29 February 2024 / Online: 1 March 2024 (10:30:13 CET)

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

Frequency dependent mass or damping or stiffness, fractional inertia or damping or restoration force, equivalent motion equation, multi-fractional Euler-Bernoulli beam

Engineering, Mechanical Engineering

* All users must log in before leaving a comment