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A new technique is proposed to investigate the response of Van der Pol-Duffing (V-D for short) oscillator to a combination of harmonic and random excitations in the primary resonant frequency region. The analytical approach is based on the stochastic averaging method and equivalent linearization method. The stochastic averaging is applied to the original equation transformed into Cartesian coordinates. Then the resulting nonlinear averaged equations are linearized by the equivalent linearization method so that the equations obtained can be solved exactly by the technique of auxiliary function. Numerical results show that the proposed approximate technique is an effective approach to solving the V-D equation. Although the technique has been used for the V-D equation in the paper, however, it can also be used to solve many other nonlinear oscillators.

Van Der Pol-Duffing oscillator under combined harmonic and random excitations