A variable-coefficient harmonic balance method for the prediction of quasi-periodic response in nonlinear systems

Quasi-periodic responses arise from various nonlinear dynamic systems under a single-frequency excitation. A variable-coefficient harmonic balance method is proposed for the prediction of quasi-periodic responses. The key point of this method is that the quasi-periodic response is described as a truncated trigonometric series with time-periodic Fourier coefficients. In other words, quasi-periodic responses are treated in a “cascade” of frequency base. Harmonic terms in the nonlinear system are separated and balanced with respect to each basic frequency. Numerical examples reveal that this method is efficient in predicting such quasi-periodic responses, which contain an unknown frequency component.