Free vibration analysis of a twisted beam using the dynamic stiffness method

An exact dynamics stiffness matrix is developed and subsequently used for f ree vibration analysis of a twisted beam whose flexural displacements are c oupled in two planes. First the governing differential equations of motion of the twisted beam undergoing free natural vibration are derived using Ham ilton's principle. Next the general solutions of these equations are obtain ed when the oscillatory motion of the beam is harmonic. This is followed by application of boundary conditions for displacements and forces, which ess entially leads to the formation of the dynamics stiffness matrix of the twi sted beam relating harmonically varying forces with harmonically varying di splacements at its ends. The resulting dynamic stiffness matrix is used in connection with the. Wittrick-Williams algorithm to compute natural frequen cies and mode shapes of a twisted beam with cantilever end condition. These are compared with previously published results to confirm the accuracy of the method, and some conclusions are drawn. (C) 2001 Elsevier Science Ltd. All rights reserved.