HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic  balance

Košata, Jan; Pino, Javier del; Heugel, Toni L.; Zilberberg, Oded

doi:10.21468/scipostphyscodeb.6

Cited by 8 publications

(2 citation statements)

References 94 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, the numerical time trace exhibits high harmonic generationthis cannot be described by the RWA, regardless of which operators are used. We remark that the same limitation applies to related methods which also rely on truncation in Fourier space, such as Floquet theory [25,53], harmonic balance [51], and Krylov-Bogolyubov averaging [54]. Hence, the relevant benchmark for the RWA solutions is the Fourier component x ω at frequency ω of the time trace.…”

Section: Example: Duffing Oscillatormentioning

confidence: 98%

See 1 more Smart Citation

Fixing the rotating-wave approximation for strongly detuned quantum oscillators

Košata

Leuch

Kästli

et al. 2022

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

Periodically driven oscillators are commonly described in a frame corotating with the drive and using the rotating-wave approximation (RWA). This description, however, is known to induce errors for off-resonant driving. Here, we show that the standard quantum description, using the creation and annihilation of particles with the oscillators' natural frequency, necessarily leads to incorrect results when combined with the RWA. We demonstrate this on the simple (quantum) harmonic oscillator and present an alternative operator basis that reconciles the RWA with off-resonant driving. The approach is also applicable to more complex models, where it accounts for known discrepancies. As an example, we demonstrate the advantage of our scheme on a driven quantum Duffing oscillator.

show abstract

Section: Example: Duffing Oscillatormentioning

confidence: 98%

“…We can now search for stationary solutions in either of the rotating frames 14) and ( 15) generate a cubic polynomial condition which has up to three solutions [4,51,52] [see Fig. 2(a)].…”

Section: Example: Duffing Oscillatormentioning

confidence: 99%

Fixing the rotating-wave approximation for strongly detuned quantum oscillators

Košata

Leuch

Kästli

et al. 2022

Phys. Rev. Research

Self Cite

View full text Add to dashboard Cite

show abstract

A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators

2022

View full text Add to dashboard Cite

Models for nonlinear vibrations commonly employ polynomial terms that arise from series expansions about an equilibrium point. The analysis of symmetric systems with cubic terms is very common, and the inclusion of asymmetric quadratic terms is known to modify the effective cubic nonlinearity in weakly nonlinear systems. The net effect is a monotonic dependence of the vibration frequency on the amplitude squared in both cases. However, in many applications, such a monotonic dependence is not observed, necessitating the use of techniques for strongly nonlinear systems or the inclusion of higher-order terms in a weakly nonlinear formulation. In either case, the analysis involves very tedious and/or numerical approaches for determining the system response. In the present work, we propose a method that is a hybrid of the methods of averaging and harmonic balance, which provides, with relatively straightforward calculations, good approximations for the amplitude-frequency dependence and for the steady-state response of damped, driven vibrations, including information about overtone harmonics and stability. The method is described, and general results are obtained for an asymmetric system with up to quintic nonlinear terms. The results are applied to a numerical example and validated using simulations. This approach will be useful for analyzing various systems with higher-order polynomial nonlinearities.

show abstract