As described earlier in Chapter 3, Yntema developed a collection of charts for rapidly estimating the natural frequencies of rotating beams for two types of mass and stiffness distributions: 1) concurrent linear distributions of both mass and stiffness, and 2) constant mass and stiffness distributions, but with a concentrated tip mass. This appendix presents a reproduction of the original charts from NACA TN 3459 (see Figs. B.1 B.10). The charts are organized according to configuration (hinged and cantilever inboard constraint) and with regard to mass distribution (linear variation of properties and concentrated mass at the end of the beam).

Figure B.1: Bending frequency coefficients a _n for hinged beams with linear mass and stiffness distributions.

Figure B.2: Zero offset Southwell coefficient for hinged beams with linear mass and stiffness distributions.

Figure B.3: Offset correction factors for Southwell coefficients for hinged beams with linear mass and stiffness distributions.

Figure B.4: Bending frequency coefficients a _n for cantilever beams with linear mass and stiffness distributions.

Figure B.5: Zero offset Southwell coefficient for cantilever beams with linear mass and stiffness distributions.

Figure B.6: Offset correction factors for Southwell coefficients for cantilever beams with linear mass and stiffness distributions.

Figure B.7: Bending frequency coefficients for nonrotating uniform hinged beams with a mass at the tip, r = tip mass/beam mass.

Figure B.8: Zero offset Southwell coefficients for a uniform hinged beam with a mass at the tip, r = tip mass/beam mass.

Figure B.9: Bending frequency...