Effect of Dead Loads on Natural Frequencies of Beams

Abstract

The effect of dead loads on the natural frequencies of uniform elastic beams is examined by means of a governing equation that takes into account the effect of dead loads. First, a governing equation including the effect of dead loads is presented briefly. Second, the effect of dead loads on natural frequencies is confirmed by the results of numerical computations using the Galerkin method for simply supported and fixed beams. It is shown that the natural frequencies are raised when the effect of dead loads is included. Third, the natural frequencies for simply supported beams, including the effect of dead loads, are presented in a closed‐form solution by means of suitable assumptions. The solution shows good agreement with the results obtained from the Galerkin method. The key physical factors governing the effect of dead loads in simply supported beams are extracted from the proposed solution.