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Hybrid models for the analysis of complex dynamic systems

  • Full or part time
  • Application Deadline
    Thursday, August 01, 2019
  • Funded PhD Project (Students Worldwide)
    Funded PhD Project (Students Worldwide)

Project Description

During the last five decades the Statistical Energy Analysis (SEA) has been successfully used to deal with a wide range of mechanical, aerospace and marine engineering applications. Based on the simple concept of diffusion and transport, commonly associated to the heat transfer, the SEA aims to model the flow of vibrational energy between an arbitrary number of subsystems which are generally part of a complex structures. It turned out to be an extremely powerful tool when analysing the dynamic behaviour of structures subjected to externally imposed vibration sources acting from the medium to high frequency range. The most obvious reason which lies behind the application of the SEA has to be found in the unavoidable uncertainty about the geometry, materials and other structural details introduced during the manufacturing process as well as environmental changes and boundary conditions. Consequently, from the medium to high frequency range, where the sensitivity of the modal resonance frequencies is relevant, the use of highly detailed deterministic mathematical models, such as the Finite Element Method (FEM), amongst others, become unreliable, and SEA-based computational methods have to be employed.

However, on the other hand, the use of the classical SEA is essentially limited to the high-frequency range. Problems occur when dealing with the mid-frequency range where both SEA and FE may lead to inaccurate response of the system for opposite reasons. In order to overcome this drawback, hybrid models can be developed [1,2]. These methods allow the combination of the statistical description (SEA) of certain subsystems of a complex system with the deterministic description (FE) of others. By virtue of this approach it is possible to properly determine the response of highly complex dynamic systems with no loss of accuracy in the mid-frequency range where some components of the system are small if commensurate to a wavelength, then prone to be modelled deterministically, and some others are large when compared with a wavelength, thus amenable to be treated statistically.

In this context, the present project aims to extend and generalise the existing hybrid methods by combining new advanced computational techniques, such as meshless methods, for the modelling of the deterministic components, and the SEA for the non-deterministic ones. Moreover, the modelling of the former will be enriched by the introduction of geometrical nonlinearities. The development of the new nonlinear nondeterministic hybrid formulation (NlNdHF) will allow the analysis of complex dynamic systems where the structural vibration and the associated sound radiation and transmission play a fundamental role. Harmonic as well as random external excitations will also be taken into account. The successful development and use of the proposed NlNdHF will allow a better understanding of the nonlinearities in structural dynamics [3] and will pave the way for possible exploitation of the latter for design purposes.

The applicant is required to have achieved a 1st or 2.1 degree in an engineering discipline, with genuine interest and ability in Matlab coding and theoretical/numerical experience in vibration and dynamics. Direct knowledge of the Statistical Energy Analysis (SEA) would be desirable, though not essential.

Funding Notes

The successful applicant will receive the School of Engineering Bursary award, consisting of tuition fee waiver for the 3 years of the programme.


[1] V. Cotoni, P. Shorter, and R. S. Langley, Numerical and experimental validation of a hybrid finite element-statistical energy method., Journal of Acoustical Society of America, 122 (1), 259–270, (2007).

[2] F. A. Fazzolari and R. S. Langley. Nonlinear hybrid models: development, validation and assessment, Report, Engineering Nonlinearity Project (EP/K003836/1) (EPSRC-funded).

[3] Worden, K., and Tomlinson, G. R., Nonlinearity in structural dynamics, IoP publishing, London, UK (2001).

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