Free vibration analysis of Euler-Bernoulli beams modeled by spatial-fractional differential equation

In this article, a more accurate dynamic model of Euler-Bernoulli beam is proposed, based on the spatialfractional derivatives. Firstly, the governing differential equation is derived. After that, this equation is solved by two different methods: the first method uses only the left fractional derivative, while the second method tends to use both the left and right fractional derivatives, simultaneously. In the second method, the location of the "switching point" which connects the left and right derivatives is treated as a variable parameter. The effect of this parameter is investigated by analyzing several beams. As numerical results, the natural frequencies and mode shapes of beams with different boundary conditions are presented.