According to the nonlinear dynamic equations of motion for slender cantilever beams axially excited by narrow-band random processes of the base,a set of nonlinear modulation equations for the principal parametric resonances is developed based on the method of multiple scales.

The method of multiple scales was used to solve directly the nonlinear differential equations and to derive the nonlinear modulation equation for the principal parametric resonance.

The method of multiple scales combined with the Cartesian transformation is used solve to the nonlinear differential equations and derive a set of nonlinear modulation equations for the principal parametric resonance of the first mode and 3:1 internal resonance between the first two modes.

By means of the average method for nonlinear vibration analysis, the amplitude frequency bifurcation equation of combined resonance system is ob.

The combination resonance behaviors of a spur gear pair with various non-linear factors such as time-varying stiffness, transmission error and tooth backlash are investigated by means of multi-scale approach.

The method of multiple scales and singularity theory are used to investigate the combination resonance and bifurcation of a nonlinear vehicle suspension system with multi-frequency excitations.

The combination resonances of an elastic linkage, which is a nonlinear dynamic system with multi degrees of freedom, are studied by the method of mutiple scales.

The union of the error correcting code and parameter-induced stochastic resonance(PSR) was proposed to reduce the bite error rate(BER) of the digital signal processing.