Professor Maria Heckl

Title: Professor of Engineering Mathematics
Phone: (+44) 01782 733423 Internal: 33423
Location: MacKay Building Room 2.23
Contacting me: Try my office or fix an appointment by e-mail

I have been a Lecturer in Applied Mathematics at Keele since 1992, and Senior Lecturer since 2001. With my background in Physics (Masters) and Engineering (PhD), I am keen to apply mathematics to real-world problems. My research interest is in mathematical modelling of acoustic phenomena and applies primarily to noise control and non-destructive testing. My research projects include:

- Combustion noise and thermoacoustics (funded by the European Commission)

- Sound propagation across tube bundles in nuclear reactors (funded by industry and EPSRC)

- Sound transmission of profiled cladding on industrial buildings

- Rolling noise from railways (industrially funded)

- Curve squeal by train wheels (EPSRC funded)

 On the teaching front, I have made a number of films on wave-related phenomena, the most recent being a 20 minute DVD on “Dispersion of waves”.

My current research project is on noise produced by flames in combustion systems, in particular gas turbines and domestic heaters. This is a topic of great practical importance because the development of low-pollution combustion systems is hampered by a phenomenon called “thermo-acoustic instability”. Such an instability is caused by a feedback between the acoustic field in the combustor and the heat release from the flame, and it leads to oscillations of increasing amplitude (see figure below), which can become so extreme that they cause severe structural damage.

Recently, I have secured two major research grants (acronyms: TANGO and LIMOUSINE) on this topic from the European Commission.


Name: Thermo-acoustic and Aero-acoustic Nonlinearities in Green combustors with Orifice Structures
Dates: 1 November 2012 – 31 October 2016
: 3.73 Million
Who is involved: Network of 9 partners, supervising 14 PhD students and 1 post-doc
Web address:  


Name: LIMit cycles of thermo-acOUStic oscillations in gas turbINE combustors
Dates: 1 October 2008 – 30 September 2012
4.15 Million
Who is involved: Network of 13 partners, supervising 17 PhD students and 3 post-docs
Web address:

As the coordinator, I play an important role in TANGO; also I am the supervisor of two PhD students and one post-doc. In the LIMOUSINE project, I acted as deputy coordinator and supervised two PhD students and one post-doc.



Time history of the acoustic pressure of a thermo-acoustic instability, ending in a limit cycle



Heckl, Maria A. (2002) Coupled waves on a periodically supported Timoshenko beam, Journal of Sound and Vibration, 252(5), pp. 849-882.

Heckl, Maria A. (2002) Curve squeal of train wheels: Unstable modes and limit cycles, Proceedings of the Royal Society, Series A, 458, pp. 1949-1965.

Heckl, Maria A. and Howe, M.S. (2007) The Rijke tube: Green’s function approach in the time and frequency domain, in: Proceedings of the 14th International Congress on Sound and Vibration, 9-12 July 2007, Cairns, Australia, 8pp.

Heckl, Maria A. and Howe, M.S. (2007) Stability analysis of the Rijke tube with a Green’s function approach, Journal of Sound and Vibration, 305, pp. 672-688. DOI:

HECKL, Maria A. (2010) "The Rijke tube: Green’s function approach in the frequency domain", Acta Acustica united with Acustica, 96(4), pp. 743-752.

Heckl, Maria A. (2013, in press) "Analytical model of nonlinear thermo-acoustic effects in a matrix burner", to appear in Journal of Sound and Vibration.