Free Vibration of Elastic Timoshenko Beam on Fractional Derivative Winkler Viscoelastic Foundation

Abstract:

The fractional derivative Winkler viscoelastic foundation model is established by introducing the concept of fractional derivative. The control equations of free vibration of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are also built by considering the shear deformation and rotary inertia, and the control equations of elastic Timoshenko beam are decoupled by using the deformation function and considering the properties of fractional derivative, and the expressions of deflection and section corner of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are obtained. The influences of fractional derivative order and shear shape factor on the free vibration of elastic Timoshenko beam are discussed by numerical example.

• Periodical: Advanced Materials Research (Volumes 368-373)
• Pages: 1034-1037
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.368-373.1034
• Online since: October 2011
• Authors: Qi Fang Yan, Zi Ping Su
• Keywords: Fractional Derivative, Free Vibration, Timoshenko Beam, Viscoelsatic

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