The problem of forced vibration of uniform Bernoulli-Euler beam with elastically supported ends due to the moton of the base is solved by normal mode approach. The motion of the base is random and its auto-spectrum is assumed to be white. Root mean square stresses in the beam for various elastically supported ends are calculated.
Change of the root mean square stress in the beam owing to change of the stiffness of the elastically supported ends is observed. The torsional spring stiffness of the supporter which minimize the maximum root mean square stress in the beam in the case of the given compressive spring stiffness is found. The relationship among the optimal torsional spring stiffness and the maximum root mean square stress in the beam in that case and the compressive spring stiffness is observed.