In the present paper, a new analytical technique is introduced for obtaining approximate periodic solutions of Helmholtz-Duffing oscillator. Modified Harmonic Balance Method (MHBM) is adopted as the solution method. A classical harmonic balance method does not apply directly for solving Helmholtz-Duffing oscillator. Generally, a set of difficult nonlinear algebraic equations is found when MHBM ...

This paper presents the non-linear dynamic analysis of a flexible unbalanced rotor supported by ball bearings. The rolling element bearings are modeled as two-degree-of-freedom elements where the kinematics of the rolling elements are taken into account, as well as the internal clearance and the Hertz contact non-linearity. In order to calculate the periodic response of this non-linear system, ...

In this paper, an analytical technique has been developed based on a modified harmonic balance method to determine higher-order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term, is an anti-symmetric and quadratic term. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these al...

A 30 W LDMOS is modeled using a 5th order polynomial model. The polynomial model is compared to the largesignal MET model using harmonic balance, and as the results agreed very well, the polynomial model was imported to a numerical Volterra simulator to find out the dominant cause of distortion for a class A biased amplifier. The characterization technique is briefly discussed.

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...

The excitation-induced stability (EIS) phenomenon in a harmonically excited bistable Duffing oscillator is studied in this paper. Criteria to predict system and excitation conditions necessary to maintain EIS are derived through a combination of the method of harmonic balance, perturbation theory, and stability theory for Mathieu’s equation. Accuracy of the criteria is verified by analytical an...

In this paper the seismic response of linear behaving structures resting on compliant soil is addressed through application Preisach formalism to capture nonlinearities. The novel model hysteresis for nonlinear soil-structure interaction problems explored study a real structure. Through harmonic balance procedure, furthermore, simplified springs and dashpots are derived in closed form ready acc...

Dynamics, control, and stability of roll oscillations a biased ship in regular sea waves are investigated. The under oscillation is modelled as the classical Helmholtz–Duffing oscillator with strongly nonlinear asymmetric restoring moment characteristics. incremental harmonic balance method, amended pseudo-arc-length continuation approach, employed to obtain uncontrolled controlled frequency re...