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

Figure 2

A free-free P-taper conic shaft composed of 𝑝 conic shaft segments (denoted by (1),(2),…,(𝑖),…,(𝑝)) and carrying one rigid disk with polar mass moment of inertia 𝐽_𝑖̂ and one torsional spring with stiffness 𝑘_𝑡,𝑖 at each node 𝑖 (𝑖=0,1,2,…,𝑝).