Detuned multiple scale analysis for improving high-amplitude prediction of nonlinear systems

Combined with a frequency detuning idea, i.e., linearization of nonlinear systems around its nonlinear response frequency rather than traditional linear natural frequency, a detuned multiple scale method (dMSM) is investigated by a full evaluation of its performance when being applied to cubic nonlinear systems with either geometrically cubic stiffness or cubic damping, i.e., a hinged–hinged beam and a generalized Van der Pol oscillator. By detailed comparison with standard MSM and focusing on frequency response and backbone curves, it is found that (detuned) dMSM demonstrates a superior performance in prediction of high-amplitude nonlinear behaviors (with weakly nonlinear assumption still valid), for both a geometrically cubic beam and a cubic damped oscillator.