Modal analysis and shape optimization of rotating cantilever beams

When a cantilever beam rotates about an axis perpendicular to its neutral axis, its modal characteristics often vary significantly. If the geometric shape and the material property of the beam are given, the modal characteristic variations can be accurately estimated following a well-established analysis procedure employing assumed mode method or finite element method. In many practical design situations, however, some modal characteristics are usually specified as design requirements and the geometric shape that satisfies the requirements needs to be found. In the present study, certain modal characteristic requirements such as maximum or minimum slope natural frequency loci are specified and the geometric shapes that satisfy the requirements are obtained through an optimization procedure.