Quasi-periodic responses composed of multiple base frequencies widely exist in science and engineering problems. The harmonic balance (MHB) method is one the most commonly used approaches for such However, it limited by low-order estimations due to complex symbolic operations practical uses. Many variants have been developed improve MHB method, among which time domain MHB-like methods are regar...

A qualitative method to verify the presence of parametric oscillations at ${f_{0}}/{2}$ in power amplifiers (PAs) is presented and validated. It relies on simultaneous application fundamental subharmonic tones trigger possible can be implemented any commercial harmonic balance solver without requiring external software that may expensive or however not available designer. Wide applicability gua...

This article presents a Harmonic Balance Method-based numerical strategy to provide qualitative characterization of compressor blade’s dynamics when structural contacts occur with the surrounding casing. The mitigation Gibbs phenomenon follows two-pronged approach: (1) regularization unilateral contact law and (2) adjustment Fourier coefficients by means Lanczos filtering technique. In order va...

The non-uniform air gap in an electrical machine caused by rotor eccentricity creates an asymmetrical flux-density distribution in the air gap. This can affect the nominal torque produced by the machine. Eccentricity also produces forces that act on the rotor which may also have an effect on the torque. Thus, it is important to know how the torque of the machine behaves. In this paper, the torq...

The harmonic content of periodic solutions in ODEs is obtained using standard techniques of harmonic balance and the fast Fourier transform (FFT). For the first method, the harmonic content is attained in the vicinity of the Hopf bifurcation condition where a smooth branch of oscillations is born under the variation of a distinguished parameter. The second technique is applied directly to numer...