Harmonic Balance Method Used for Calculating the Steady State Oscillations of a Simple One-Cylinder Cold Engine

Tribute to Joël Gilbert

“…From the theoretical and numerical point of view, the calculations of regimes (permanent or transient) and their stability remain a challenge. J. Gilbert was one of the first to introduce in acoustics the method of harmonic balance including the unknown playing frequency from methods developed in electromagnetism for microwaves [1,17]. However, there are other types of non-linearities, which also greatly interested him.…”

“…It is interesting for factors and musicians, but although linear, it is complicated [27,31,40]. He was also interested in anything that could closely or remotely resemble a trombone: an elephant, a moose, a deer [44,46,53], but also a thermo-acoustic engine or an internal combustion engine [17,26,45]. Last year he published with Springer with Murray Campbell and Arnold Myers a sum called "The science of brass instruments", which combines knowledge in acoustics and organology [58].…”

Dynamics of dry friction damping in gas turbines: literature survey

“…This is a frequency-domain method which is time efficient compared to time-domain methods. This type of method is useful for the analysis of systems with steady-state solutions (Sinha and Griffin, 1984;Griffin and Sinha, 1985;Albertson and Gilbert, 2001;Petrov and Ewins, 2003;Petrov, 2005;Legrand et al, 2006). The harmonic balance method assumes that the input harmonic excitation in a system consists of a number of steady-state sinusoids and therefore its response is also harmonic and a sum of steady-state sinusoids with the same frequency as that of excitation, while the amplitude and phase remain unknown and the friction force is calculated in terms of these unknowns.…”

“…HB methods have been used to solve nonlinear dynamical problems for many years. Their application to various practical problems have been discussed in a number of papers (Sinha and Griffin, 1984;Griffin and Sinha, 1985;Albertson and Gilbert, 2001;Petrov and Ewins, 2003;Petrov, 2005). Ferri and Dowell have done a significant amount of work in friction damping analysis using the HB method in joint papers Dowell, 1985, 1988) and separate papers (Dowell, 1983;Ferri, 1986).…”

The acoustics of racing engine intake systems

“…[11][12][13][14][15][16][17][18][19] calculate U s ; U e ; Z e ; Z 1 ; U 1 ; P 1 whereas in the uncoupled hybrid method used here Z 1 is calculated, Z e is neglected, U 1 is estimated and these are used to calculate an approximate P 1 : An estimate for U 1 is calculated in two steps. A first estimate is obtained from…”