Analytical Solution for Transverse Vibration of a Composite Euler-Bernoulli Beam Including Several Concentrated Masses

Transverse vibration of a composite Euler-Bernoulli beam with any arbitrary concentrated masses is developed and analytically solved in this paper. First, dynamic governing equations of a cross-ply beam with taking into account of number, location and amount of concentrated masses as well as the effects of torsional behavior of composite layup (due to bending-twisting coupling) are derived. Concentrated masses are modeled by delta Dirac function. Then, the governing equations are solved for two different boundary conditions (simplysupported, clamped-free) to obtain frequency response and mode shapes. The results of the developed model are validated by the available analytical results in the literature. Thus, the effects of number, location and amount of concentrated masses on the torsional-bending vibration of a composite beam can be investigated.