Accurate higher-order approximations to frequencies of nonlinear oscillators with fractional powers

An improved harmonic balance (HB) method is been presented to construct more accurate approximations to frequencies of oscillators with non-linear fractional powers. Unlike the classical HB method, linearization is carried out prior to harmonic balancing thus resulting in simple linear algebraic equations instead of complicated nonlinear algebraic equations. Hence, we are able to establish the approximate frequencies for the oscillators more directly. These approximate results are valid for various fractional powers including the limiting case of vanishing power. Comparing with previous approximate solutions, the approximate solutions derived here are more accurate with respect to established exact solutions.