A root-finding technique to compute eigenfrequencies for elastic beams

In this manuscript a method to compute eigenfrequencies for elastic beams is presented. For beam modeling, three fundamental effects are considered: bending, rotary inertia and shear deformation. The method consists on enclosing each eigenfrequency in an interval where the characteristic function is monotonic. Then, a root finding technique is used to compute the eigenfrequency to any desired accuracy. The method is applied successfully to equations involving bending and either rotary inertia or shear deformation.