Torsional Vibrations of a Conic Shaft with Opposite Tapers Carrying Arbitrary Concentrated Elements

Figure 4

(a) The PN-taper conic shaft (𝐴𝐵𝐶) is replaced by 𝑛_𝑒 uniform circular shaft elements. (b) The average diameter 𝑑^∼_𝑗 (𝑗=1,2,…,𝑛_𝑒) for the 𝑗th uniform circular shaft element in the positive-taper part 𝐴𝐵 is determined by 𝑑^∼_𝑗=(𝑑²_𝑗+1𝑥_𝑗+1−𝑑²_𝑗𝑥_𝑗)/(3Δ𝑥_𝑗).

(a)

(b)