LATERAL VIBRATION OF A CENTRIFUGALLY TENSIONED UNIFORM EULER-BERNOULLI BEAM

This paper describes the lateral vibration of a uniform Euler-Bernoull i beam that is doubly symmetric in cross-section and attached radially to the outside of a rotating hub. It is assumed that a principal axis of the beam is parallel to the axis of rotation and thus the out-of-p lane and in-plane vibrations are uncoupled. The equation of motion is derived on the basis that the attachment at the hub is radially restra ined. The general solution of the mode shape equation is expressed as the superposition of four linearly independent functions. Clamped, pin ned and free boundary conditions are considered. It is shown that the natural frequencies depend not only on the natural and/or geometric bo undary conditions but also on which of the two boundaries is radially free. The first three dimensionless natural frequencies are tabulated for out-of-plane vibration for six combinations of the simple boundary conditions and for a range of offset parameters and dimensionless rot ational speed. From the tables it is possible to deduce the dimensionl ess natural frequencies for in-plane vibrations. For parameters not li sted, interpolated results are accurate to within 0.3%. It is hoped th at the tabulated results will serve as data for development of frequen cies for problems with more complicated flexural rigidity and/or mass distribution.