Free vibrations of simply supported beams using fourier series

Abstract EN

Fourier series will be utilized for the solution of simply supported beams with different loadings in order to arrive at a free vibration.

The equation of the free vibration is σ2y/(σt2 ) + σ4y/σx4 One of the methods of solving this type of equation is the separation of the variables which assumes that the solution is the product of two functions, one defines the deflection shape and the other defines the amplitude of vibration with time.

Modes of deflection with and without time along the beam were drawn for certain cases.

Good agreement has been obtained between the results of the present study and that determined by Timoshinko [11].