Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method

Starting from the governing differential equations of motion in free vibrat ion, the dynamic stiffness matrix of a uniform rotating Bernoulli-Euler bea m is derived using the Frobenius method of solution in power series. The de rivation includes the presence of an axial force at the outboard end of the beam in addition to the existence of the usual centrifugal force arising f rom the rotational motion. This makes the general assembly of dynamic stiff ness matrices of several elements possible so that a non-uniform (or tapere d) rotating beam can be analyzed for its free-vibration characteristics by idealizing it as an assemblage of many uniform rotating beams. The applicat ion of the derived dynamic stiffness matrix is demonstrated by investigatin g the free-vibration characteristics of uniform and non-uniform (tapered) r otating beams with particular reference to the Wittrick-Williams algorithm. The results from the present theory are compared with published results. I t is shown that the proposed dynamic stiffness method offers an accurate an d effective method of free-vibration analysis of rotating beams. (C) 2000 A cademic Press.