FREE-VIBRATION OF AXIALLY LOADED COMPOSITE TIMOSHENKO BEAMS USING THEDYNAMIC STIFFNESS MATRIX-METHOD

The free vibration analysis of axially loaded composite Timoshenko bea ms is carried out by using the dynamic stiffness matrix method. This i s accomplished by developing an exact dynamic stiffness matrix of a co mposite beam with the effects of axial force, shear deformation and ro tatory inertia taken into account, i.e. it is for an axially loaded co mposite Timoshenko beam. The theory includes the (material) coupling b etween the bending and torsional modes of deformations which is usuall y present in laminated composite beams due to ply orientation. An anal ytical expression;for each of the elements of the dynamic stiffness ma trix is derived by rigorous application of the symbolic computing pack age REDUCE. Use of such expressions leads to substantial savings in co mputer time when compared with numerical methods usually adopted in th e absence of such expressions. The application of the dynamic stiffnes s matrix is demonstrated by investigating the free vibration character istics of an example composite beam for which some comparative results are available. The solution technique used to yield the natural frequ encies is that of the Wittrick-Williams algorithm. The effects of axia l force, shear deformation and rotatory inertia on the natural frequen cies are demonstrated. The theory developed has applications to compos ite wings and helicopter blades. (C) 1998 Elsevier Science Ltd. All ri ghts reserved.