Thomas Breunung

Haller Group     IMES    ETH

About Photo

Hi, I’m Thomas.

I am a fourth year PhD student working on nonlinear dynamical systems supervised by Prof. George Haller.

I analyze complex dynamical systems. My research goal is to understand the fundamental dynamic behavior of nonlinear mechanical systems. For this purpose I extend existing methods, program computational tools and perform fundamental analytical research. My applications focus mainly on mechanical vibrations, such as vibration supressing, stability analysis and calculation of the forced response (FRF plots).

My Research

Time-varying Spectral Submanifolds
Time-varying Spectral Submanifolds

Spectral submanifolds (SSMs) have recently been shown to provide exact and unique reduced-order models for nonlinear unforced mechanical vibrations. We have extended these results to periodically or quasi-periodically forced mechanical systems, and obtained analytic expressions for forced responses and backbone curves on modal (i.e. two dimensional) time-dependent SSMs. A judicious choice of the parametrization of these SSMs allows us to simplify the reduced dynamics considerably. We have demonstrated our analytical formulae on three numerical examplesand compare them to results obtained from availablenormal-form methods.


T. Breunung & G. Haller, Explicit backbone curves from spectral submanifolds of forced-damped nonlinear mechanical systems. Proc. R. Soc. A 474 (2018) 20180083. doi

Fast Computation of Steady-State Response
Fast Computation of Steady-State Response

We have develped an integral equation approach that to enable fast computation of the response of non-linear multi-degree-of-freedom mechanical systemsunder periodic and quasi-periodic external excitation. The kernel of this integral equation is a Green’s function that we compute explicitly for general mechanical systems. We derive conditions under which theintegral equation can be solved by a simple and fast Picard iteration even for non-smooth mechanical systems. The convergence of this iteration cannot be guaranteed for near-resonant forcing, for which we employ a Newton–Raphson iteration instead, obtaining robustconvergence. We further show that this integral equation approach can be appended with standard continuation schemes to achieve an additional, significant performance increase over common approaches to com-puting steady-state response.


S. Jain, T. Breunung, & G. Haller, Fast computation of steady-state response for high-degree-of-freedom nonlinear systems Nonlinear Dynamics 97, 1 (2019) 313-341. doi

Existence of Periodic Orbits
Existence of Periodic Orbits

While periodic responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori existence criteria for mechanical systems hinders definitive conclusions about periodic orbits from approximate numerical methods, such as harmonic balance. We have established results guaranteeing the existence of a periodic response without restricting the amplitude of the forcing or the response. Our results provide a priori justification for the use of numerical methods for the detection of periodic responses. We illustrate on examples that each condition of the existence criterion we discuss is essential.


T. Breunung & G. Haller, When does a periodic response exist in a periodically forced multi-degree-of-freedom mechanical system? Nonlinear Dynamics 98, 3 (2019) 1761-1780 doi

Random Dynamical Systems
Random Dynamical Systems

We have developed a method to clarify the role of deterministic invariant manifolds if small white noise excitation is added. To this end we have extended the notion of a transport barrier from fluid dynamics to the mechanical vibrations setting. Thereby, we can calrify the relevance of normally hyperbolic invariant manifolds and spectral submanifolds under small whithe noise perturbations.

Work in progress with

F. Kogelbauer & G. Haller

Academic Experience

ETH Zürich
JUL 2016 -

PhD candidate working on nonlinear mechanical vibrations.

TU Darmstadt
OCT 2009 - MAY 2016

Studied Mechanical and Process Engineering;
Obtained Degrees: Bachelor & Master of Science.

Masterthesis on stability analysis of linear systems with time-periodic coefficients.

UC Berkeley
AUG 2013 - MAY 2014

Semester abroad at the Department of Mechanical Engineering

Meet me at the Conferences

ENOC 2020 , Lyon, France
5.-10. JUN 2020

The relevance of spectral submanifolds and slow manifolds for randomly excited nonlinear mechanical systems

IMAC XXXVIII, Houston, Texas, US
10.-13. FEB 2020

The relevance of nonlinear normal modes for randomly excited nonlinear mechanical systems

ICoNSoM 2019, Rome, Italy
16.-19. JUN 2019

Existence of the steady state response of periodically forced dissipative nonlinear mechanical systems

My Latest Publications


Leonhardstrasse 21 LEE M226

8092 Zürich, Switzerland


Phone: +41 44 633 83 56

Mail: Thomas Breunung