Analysis of Effect of Dead Loads on Natural Frequencies of Beams Using Finite-Element Techniques

In this paper, a conception of load-induced stiffness matrix is developed, and a beam element for using the finite-element method, which takes into consideration the stiffening effect of dead loads, is proposed. The element stiffness matrices including the effect of dead loads are derived according to Hamilton's principle. The effect of dead loads on natural frequencies is analyzed by the finite-element method for simply supported and cantilever beams; and two types of dead load, uniform load per unit length and concentrated load, are considered in calculations. It is shown that the natural frequencies increase when the effect of dead loads is included, and that the effect is more significant for cantilever beams than for simply supported beams. The validity of the proposed procedure is confirmed by the numerical examples. Although the results obtained by the finite-element method are in agreement with those given by Takabatake, the proposed method with a finite-element-method formulation is more easily applied to practical structures under various support conditions and various types of dead loads.