This paper is concerned with the study of third order quadratic and autonomous systems and the interest is oriented to the stable periodic oscillations. From the “jerk” equation model, the classes of minimal complexity presenting a Hopf bifurcation are derived and their local characterization is carried out by means of a suitable harmonic balance technique. Other possible system reductions pres...

The influence of permanent dipole moments of quantized states on intersubband second harmonic generation based on quantum-interference induced transparency in semiconductor quantum wells is explored using the harmonic balance method. The permanent moments are found to be quite important: they affect the transparency condition, especially at larger pump intensities. Hence, both the conversion ef...

In this paper, the analytical methods for approximate solutions of periodic motions to chaos in nonlinear dynamical systems are reviewed. Briefly discussed are the traditional analytical methods including the Lagrange stand form, perturbation methods, and method of averaging. A brief literature survey of approximate methods in application is completed, and the weakness of current existing appro...

Considerable work has been done on the development of advanced process control for the Electric Arc Furnace (EAF) steelmaking process. Historically, many control systems have been employed which rely on static heat balance calculations coupled with power input profiles to generate recipe driven control models. Steelmakers have desired to have continuous information about the gases exiting the f...

This paper describes a new simulation technique of nonlinear RF circuits driven by modulated signals. Based on a true mixed-mode algorithm, it allows time-domain transient analysis of the envelope, while handling the carrier behavior in frequency-domain. Being similar in scope to the previously reported Envelope Transient Harmonic Balance [1]-[3], it is not limited, though, in excitation bandwi...

This paper detects the disturbing loads in distorted and/or un-balanced three phase three wire power system. It is based on the simultaneous measurement of four non-active power quantities, which are found on the IEEE Std. 1459-2000 method. It allows, achieving better knowledge of the power system when both harmonic distortion and un-balance are present. The proposed method requires only the fu...

The recent interest in the area of the control of chaos is remarked and the various approaches to this problem presented in the literature are briefly summarized. The Harmonic Balance (HB) technique for the approximate analysis of systems with complex behaviour is outlined and the general idea of using this technique for control problems is proposed. Two possible approaches are indicated to sho...

Propagation of monochromatic elastic waves across cracks is investigated in 1D, both theoretically and numerically. Cracks are modeled by nonlinear jump conditions. The mean dilatation of a single crack and the generation of harmonics are estimated by a perturbation analysis, and computed by the harmonic balance method. With a periodic and finite network of cracks, direct numerical simulations ...

We develop a method for the accurate reconstruction of non-bandlimited finite rate of innovation signals on the sphere. For signals consisting of a finite number of Dirac functions on the sphere, we develop an annihilating filter based method for the accurate recovery of parameters of the Dirac functions using a finite number of observations of the bandlimited signal. In comparison to existing ...

A distributed modeling approach has been developed to describe the dynamic behavior of ring resonators. The model includes the effect of large amplitudes around primary resonance frequencies, material and electrostatic nonlinearities. Through a combination of geometric and material nonlinearities, closed-form expression for third-order nonlinearity in mechanical stiffness of bulk-mode ring reso...