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Conference Proceedings
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6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
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On some simple mechanical systems
governed by differential equations with fractional derivatives
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The intent is to show that the governing equation for simple mechanical systems may contain fractional derivatives. We will consider three types of oscillator to which a semi-infinite Bernoulli-Euler beam is attached. It will be shown that if the consideration is limited only to the oscillator, then the environment (i.e. a semi-infinite Bernoulli-Euler beam) adds a fractional derivative into the oscillator equation. Another system governed by the differential equation with fractional derivative is the suspension of the fluid-conveying-pipe. The eigenvector expansion method based upon transformation of the equation into a set of four first-order semidifferential equations is utilised for solving the obtained differential equation with fractional derivatives.