School of Mathematical Sciences

Research menu

Good vibrations: spectral theory to improve the accuracy of vibrational energy predictions in complex structures such as cars, aeroplanes and buildings


  • Improving the accuracy and speed of predicting vibrational energy distributions
  • Speeding up design timeframes
  • Impact on the automotive, shipbuilding and aircraft industries

 The challenge

Designs for complex structures like cars, aeroplanes and modern buildings suffer from unpredictable vibrations that lead to anything from irritating noises to dangerous structural failures. Predicting the distribution of vibrational energy in large coupled systems is an important and challenging task of major interest to industry. For example, cars contain many moving components that may produce resonances resulting in unwanted rattles, vibrations and possibly dangerous structural weaknesses.  Until recently there was no reliable method to predict vibrations at the important mid-to-high frequency ranges.

The solution

To address this, there is a need to gain accurate predictions of vibrations at the design stage. However, previous techniques are too cumbersome to be used in a fast-moving commercial design setting.  Building on ideas from Quantum Chaos, Bandtlow has contributed his expertise in spectral theory to develop a novel method that computes close approximations to these predictions but in a reasonable time. This in turn has informed inuTech’s latest product and led to enhanced performance of automobiles and aircraft.

Based in Nuremberg, inuTech is an SME targeting engineering challenges that require application of new numerical methods. As part of their work they develop products aimed at vibration prediction and have used Bandtlow’s research and methods to develop these products. Between January to March 2011, Bandtlow was based at inuTech in Nuremberg contributing to a black-box implementation of this approach, which emerged as a result of his research in operator theory.

 The collaboration and impact

Example beneficiaries of inuTech’s products are the automotive, aircraft, and shipbuilding industries. In fact, inuTech works with Range Rover, EADS, and Germanischer Lloyd, who have all expressed interest in the software.  So far, the software and consultancy expertise has been used to approach problems posed by Range Rover for shock-absorber towers of cars, by EADS for the Airbus fuselage, and by Germanischer Lloyd for the design of ship hulls. The application of Bandltow’s research ensures that resonances are minimised supporting successful design.

The algorithms developed are now stable and are able to cope with increasingly complex situations.  The improvements made to the software considerably speed up and improve the accuracy of this part of the design process, resulting in cheaper and safer cars. The founder and CEO of inuTech says: “The expertise offered by Bandtlow plays an essential role for our project to predict vibrational energy distributions in large built-up structures. The economic success of the implementation of these ideas depends crucially on his input and I am looking forward to continue this fruitful and beneficial collaboration on related projects”.

 For further information please contact:

 Dr. Oscar Bandtlow,

Dr. Wolfram Just,