Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

Figure 4

Comparisons of frequency amplitude relationships obtained with the 1st order homotopy analysis method and the 4th order Lindstedt-Poincare method for the first four modes: (a) 𝑓=0.002; (b) 𝑓=0.02; (c) 𝑓=0.04; (d) 𝑓=0.08. A: the 1st symmetric mode, B: the 1st antisymmetric mode, C: the 2nd symmetric mode, and D: the 2nd antisymmetric mode.

(a)

(b)

(c)

(d)