EXACT DYNAMIC STIFFNESS MATRIX FOR COMPOSITE TIMOSHENKO BEAMS WITH APPLICATIONS

Abstract In this paper, an exact dynamic stiffness matrix is presented for a composite beam. It includes the effects of shear deformation and rotatory inertia: i.e., it is for a composite Timoshenko beam. The theory accounts for the (material) coupling between the bending and torsional deformations which usually occurs for such beams due to the anisotropic nature of fibrous composites. An explicit analytical expression for each of the elements of the dynamic stiffness matrix is derived by rigorous use of the symbolic computing package REDUCE . It is proved that the use of such expressions leads to substantial savings in computer time when compared with the matrix inversion method. The use of this dynamic stiffness matrix to investigate the free vibration characteristics of composite beams (with or without the effects of shear deformation and/or rotatory inertia included) is demonstrated by applying the Wittrick-Williams algorithm. Numerical results for which comparative results are available in the literature are discussed.