Abstract
The equivalent linearization method based on weighted averaging is employed to obtain a approximate solution for a generalized nonlinear oscillator given in the form of $$ \ddot{u} + \alpha u + \beta u^{m} + \frac{{\gamma u^{n} }}{{\mu + \delta u^{p} }} = 0. $$ The amplitude–frequency relationship of oscillation is given in a closed-form. Accuracy of the approximate solution is verified by comparing the obtained solution with the numerical solution using the 4th-order Runge–Kutta method. Specifically, the obtained results for some special cases such as cubic-, quintic-, seventh order-Duffing oscillators, Duffing-harmonic oscillator, nonlinear oscillator with fractional nonlinearity are compared with the results achieved by the other approximate methods.
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