Abstract
Three types of suspension of a semi-infinite Bernoulli-Euler beam and a fluid-conveying pipe are considered. It is shown that the environment in the form of a semi-infinite Bernoulli-Euler beam or a fluid-conveying pipe is taken into account by adding a fractional derivative into the suspension equation. The eigenvector expansion method based upon transformation of the derived equation into a set of four semi-differential equations is utilised for solving the equations with fractional derivatives. A simple expression for the critical velocity of the fluid in the pipe is obtained. If this value is exceeded, both the pipe and its suspension become unstable.
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References
Suarez, L.E., Shokooh, A.: An eigenvector expansion method for the solution of motion containing fractional derivatives. ASME J. Appl. Mech. 64, 629–635 (1997)
Oldham, K.B., Spanier, J.: Fractional Calculus. Academic, New York (1974)
Acknowledgements
The work was supported by the joint project of the Russian Foundation for Basic Research and the National Science Council, Taiwan, grant 12-01-92000 HHC_a.
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© 2014 Springer-Verlag Wien
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Belyaev, A.K. (2014). Fractional Derivatives Appearing in Some Dynamic Problems. In: Belyaev, A., Irschik, H., Krommer, M. (eds) Mechanics and Model-Based Control of Advanced Engineering Systems. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1571-8_5
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DOI: https://doi.org/10.1007/978-3-7091-1571-8_5
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