Free transverse vibration analysis of laminated composite beams with arbitrary number of concentrated masses

Abstract

In this study, a new closed-form solution for transverse free vibration analysis of laminated composite beams (LCBs) with arbitrary number of concentrated masses is developed. The LCB is modeled based on the Euler-Bernoulli beam theory and concentrated masses are simulated considering Dirac delta function.Obtained governing equations are, then, solved semi-analytically while the frequency equation and mode shapes are extracted for two different boundary conditions, i.e., clamped-free and simply-supported. In order to verify the closed-form solution, the represented model is simplified for a beam without concentrated mass and outcomes are compared with available results in the literature. Finally, the effects of mass as well as location and number of concentrated masses on the free vibration response of the beam are investigated in detail. The results highlight that with increasing the value of point masses, the natural frequencies decrease. Also, it was revealed that the number of point masses influences on the vibration of cantilever beam more than the simply-supported one. These outcomes would practically be used to minimize detrimental effects of vibrational noises, leading to increase of the structural components' lifetime.