Application of homotopy analysis method in nonlinear oscillations

In this paper, we apply a new analytical technique for nonlinear problems, namely the Homotopy Analysis Method (Liao 1992a), to giver two-period formu las for oscillations of conservative single-degree-of-freedom systems with odd nonlinearity. These two formulas are uniformly valid for ally possible amplitudes of oscillation. Four examples are given to illustrate the validi ty of the two formulas. This paper also demonstrates the general validity a nd the great potential of the Homotopy Analysis Method.