Free vibration of composite beams - An exact method using symbolic computation

An exact dynamic stiffness matrix method has been developed to predict the free vibration characteristics of composite beams (or simple structures assembled from them) for which the bending and torsional displacements are (materially) coupled. To achieve this, an explicit expression is presented for each of the elements of the dynamic stiffness matrix of a bending-torsion coupled composite beam. This was made possible by performing symbolic computing with the help of the package Reduce. Programming the stiffness expressions in Fortran on a SUN SPARC station indicates about 75% savings in computer time when compared with the matrix inversion method normally adopted in the absence of such expressions. The derived dynamic stiffness matrix is then used in conjunction with the Wittrick-Williams algorithm to compute the natural frequencies and mode shapes of composite beams with substantial coupling between bending and torsional displacements. The results obtained from the present theory are compared with those available in the literature and discussed.