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

Figure 6

The P-taper shaft (cf. case 2 of Table 1) carrying: (a) 3 rigid disks each with 𝐽_𝑖̂=𝐽^∗/3 (𝑖=0,1,2); (b) 3 torsional springs each with 𝑘_𝑡,𝑖=𝑘^∗_𝑡/3 (𝑖=0,1,2); and (c) 3 rigid disks and 3 torsional springs each with 𝐽_𝑖̂=𝐽^∗/3 and 𝑘_𝑡,𝑖=𝑘^∗_𝑡/3 (𝑖=0,1,2). The locations of concentrated elements are 𝑥₀=3.0 m, 𝑥₁=4.0 m, and 𝑥₂=5.0 m. Besides, 𝐽^∗=5.4409436902×10⁻³ kg-m² and 𝑘^∗_𝑡=1.378230198×10⁴ Nm/rad.

(a)

(b)

(c)