The modal distribution and density of fibre reinforced composite beams

Fibre reinforced composites are extensively used in applications that exploit their high strength to weight and modulus to weight ratios. Structures made of composites can be subjected to random structural excitation that spans a significant fraction of the audible frequency range, thus exciting a large number of modes. The concept of modal density is employed when such excitation is present and it is a critical parameter for the high frequency tool, statistical energy analysis. In this paper an analytic expression, independent of boundary conditions, is derived for the modal density of fibre reinforced composite beams coupled in bending and torsion. The variation of the modal density with fibre orientation for a unidirectional fibre reinforced composite is investigated and it is seen that there exists in every frequency band an orientation that corresponds to a minimum modal density. The additive property of the modal density for discontinuous composite beam systems is also verified.