EXACT SOLUTION FOR THE FREE-VIBRATION OF AXIALLY-LOADED PRETWISTED RODS

For a pretwisted rod, in which torsional and flexural effects are deco upled, both vibration and buckling behaviour may be described by a pai r of fourth-order linear ordinary differential equations. By consideri ng the free vibration of axially-loaded pretwisted rods, a superset of the buckling and vibration equations may be obtained, and these equat ions may be solved analytically. Such solutions indicate that the rela tionship between the natural frequency and the applied load is effecti vely independent of the pretwist angle, for compressive loads and mode rate tensile loads.