Christophe Lecomte

A frequency averaging framework for the solution of complex dynamic systems

A frequency averaging framework is proposed for the solution of complex linear dynamic systems. It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework. An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions.

Zero and root loci of disturbed spring-mass systems

Models consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses are presented, including when damping is present. Several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain are presented and proved. In particular, it is shown that there exists an elliptical region in the frequency–disturbance magnitude plane from which zeros are excluded and the discrete values of the frequency and disturbance at which double poles occur are identified. A particular focus is on a local disturbance, such as when a spring or damper is modified at or between the first and last masses. It is demonstrated how, notably through normalization, the techniques and results of the paper apply to a broad category of more complex systems in physics, chemistry and engineering.

Bayesian damage localisation at higher frequencies with Gaussian process error

This paper concerns the estimation of the location (and properties) of damage in structures using Bayesian methods and Markov Chain Monte Carlo (MCMC). It is widely recognised that the consideration of uncertainty in structural dynamic systems may be essential, for example from an economic point of view (“Does is make sense to add expensive damping if it will only affect a small proportion of the vehicles we produce?”) or for critical safety purposes (“What is the risk of failure of an airplane engine due to bladed disk mistuning?”). The use of Bayesian methods appears to be a viable approach to obtain inferences about the parameters of such uncertain systems. Here we report on numerical experiments on the use of MCMC to locate a frequency dependent damage in a one-dimensional structure. Transfer function measurements subject to a Gaussian process measurement error are available. The particular structure of the resulting system matrices is then seen to have a special form which results in a semi-analytic solution method being available and a much reduced computational cost. We discuss the characteristics and efficiency of the Bayesian model and MCMC computation and highlight features in the analysis of structural dynamic systems such as higher-frequency multimodality.