It is the purpose of this paper to introduce a computer software that is developed for the analysis of general multi degree of freedom rotor bearing systems with non-linear support elements. A numerical-analytical method for the prediction of steady state periodic response of large order nonlinear rotor dynamic systems is addressed which is based on the harmonic balance technique. By utilizing ...

In this paper we will study the non-linear oscillation of a conservative system having inertia and static non-linearities. By combining the linearization of the governing equation with the method of harmonic balance, we investigate analytical approximate solutions for the non-linear oscillations of the system. Unlike the classical harmonic balance method, linearization is performed prior to pro...

This paper is a survey of the inverse scattering problem for time-harmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering” and Newton-type methods for solving the inverse scattering problem for acoustic waves, including a brief discussion of Tikhonov’s method for the numerical solution of ill-posed problems. We then proceed to prove a uniquen...

This paper deals with the accuracy of a numerical time integration scheme, the implicit Generalizedα method, when applied near resonant conditions in periodic steady-state vibrations of elastic linear and nonlinear systems. In order to evaluate errors, analytical solutions of Frequency Response Functions (FRFs) are determined by using the Harmonic Balance method in singleand two-degrees-of-free...

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic sol...

A new self-consistent dynamic electro-thermal model for power HBTs is presented coupling a circuit-oriented electrical model, fitted on experimental data, with a full frequency domain thermal model. The thermal model provides the exact frequency behaviour of the device thermal impedance through a quasi-3D approach. The electro-thermal self-consistent solution is achieved, in large-signal period...

Properties of small amplitude oscillations of the single reed woodwind instruments near the oscillation threshold are investigated. Analytical formulae with explicit dependence on the physical parameters of the instrument and instrumentist allow to determine the bifurcation point, the nature of the bifurcation, the amplitude of the first harmonics and the oscillation frequency. The model, which...

Abstract Dynamics and stability of average current control of DC-DC converters are analyzed by sampleddata modeling. Orbital stability is studied and it is found unrelated to the ripple size of the orbit. Compared with the averaged modeling, the sampled-data modeling is more accurate and systematic. An unstable range of compensator pole is found by simulations, and is predicted by sampled-data ...

A modified sum-rates method based on insights provided by an analysis given by Sridhar and Lucia (Ind. Engng Chem. Res. 28, 793-803, 1989) is presented. Newton’s method is used to accelerate the inner loop of combined mass balance and phase equilibrium equations and to solve the outer loop of energy balance equations. All partial derivative information is obtained in analytical form. Several li...