FURTHER FLEXURAL VIBRATION CURVES FOR AXIALLY LOADED BEAMS WITH LINEAR OR PARABOLIC TAPER

The curves presented cover eleven combinations of end conditions, three types of taper, all taper ratios between 0 multiplied by (times) 3 and 1, and all axial forces between minus P//c and 0 multiplied by (times) 6P//c, where P//c is the critical buckling load for pure compression and can be found from curves provided. The results cover truncated wedges which have their depth and width varying identically, so that all cross sections are similar in the sense that similar triangles are. The curves also illustrate how natural frequencies and buckling loads are altered by changing the amount and type of a member's taper while keeping its mass constant. Illustrative results show the effects of using exact Timoshenko stiffnesses instead of the Bernoulli-Euler ones.