The Behavior of the Synchronous and Asynchronous Natural Frequencies for Asymmetric Double Beams

Abstract

The effect of vibrations on asymmetric double beams is a common engineering problem in various engineering applications. In this paper, the synchronous (lower) and asynchronous (higher) natural frequencies of the asymmetric double beams are calculated using the Bernoulli-Euler method. Where the traditional methods are used to find the frequency equations at different boundary conditions, such as Pinned beam, clamped-Clamped beam, Clamped-Free beam, and Clamped-Pinned beam. The increase in the stiffness of the elastic connected layer leads to an increase in the values of the high frequencies of double beams. The greatest effect of changing the thickness of one of the upper or lower beams is for CF beams and the least effect is for CP beams. The length of the beam affects the higher and lower frequencies in high and close proportions for almost all types of beams, and the least effect is only on the higher frequencies of CF beams. The influence of the modulus elasticity change is relatively small on the lower natural frequencies of all types of beams except for CF beams, and its effect is relatively large on the higher natural frequencies of the most types of beams and comparatively less on the CF beams. The effect of varying the values of mass density is relatively small on the low natural frequencies of all types of beams except for CF beams, and its effect is comparatively large on the higher natural frequencies of all types of beams and relatively less on the CF beams.