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

Figure 8

The free-free PN-taper conic shaft carrying: (a) 5 rigid disks each with 𝐽_𝑖̂=𝐽^∗/5 (𝑖=0,1,2,3,4); (b) 5 torsional springs each with 𝑘_𝑡,𝑖=𝑘^∗_𝑡/5 (𝑖=0,1,2,3,4); and (c) 5 rigid disks and 5 torsional springs each with 𝐽_𝑖̂=𝐽^∗/5 and 𝑘_𝑡,𝑖=𝑘^∗_𝑡/5 (𝑖=0,1,2,3,4). The locations of the concentrated elements are: 𝑥_𝑖=3.0,4.0,5.0,6.0, and 7.0 m, respectively. Besides, 𝐽^∗=1.0881887380×10⁻² kg-m² and 𝑘^∗_𝑡=6.891150988×10³ N-m/rad.

(a)

(b)

(c)