Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

Figure 5

In-plane displacement fields obtained with homotopy analysis method and Lindstedt-Poincare method in the case of the first symmetric mode: (a) 𝑓=0.002, (Ω₁−𝜔₁)/𝜔₁=0.05; (b) 𝑓=0.02, (Ω₁−𝜔₁)/𝜔₁=0.25; (c) 𝑓=0.04, (Ω₁−𝜔)/𝜔₁=−0.10; (d) 𝑓=0.08, (Ω₁−𝜔₁)/𝜔₁=2.0.

(a)

(b)

(c)

(d)