On some simple mechanical systems
governed by differential equations with fractional derivatives
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.