Tutorials

During the conference tutorials will be given by renowned scholars :

1. Monday: Etienne Balmes, SDTools, France
2. Tuesday: Bob Randall, UNSW, Australia
3. Wednesay: Thibaut Detroux, NOLISYS, Belgium

Error characterization in modal analysis and model updating. An overview of tools and procedures using the Structural Dynamics Toolbox

Experimental modal analysis seeks to extract shape and resonance properties from test data. While identification algorithms have been well documented for a long time, at least under the assumption linear behavior, significant differences continue to exist in the implementation details. In particular, non-linear optimization of poles and work by sub-bands is an often overlooked necessity to avoid bias. Once modal data available, the next step is to obtain test/analysis correlation. This requires topology correlation which brings its share of errors, which despite being usually small should be addressed. Global correlation criteria, such as the MAC, are introduced next but for efficient use should be complemented by a set of procedures to localize measurement, topology and correlation errors. While the simple evaluation of correlation is often an industrial objective, the best exploitation of test results is achieved using hybrid approaches combining test with a model, which does not need to be exact to usefully complement the measurements. In particular, expansion methods estimating the full Finite Element responses from data measured at sensors are particularly useful. Energy based criteria on the model side (Minimum Dynamic Residual Expansion or the various variants of Error in Constitutive Relation) have been long known to provide excellent solutions but deployment has been scarce due to an important numerical cost. Simple model reduction strategies are shown to give excellent results for industrial models and open the way for model error localization and updating.

The tutorial is illustrated using standard procedures implemented in the Structural Dynamics Toolbox which provides experimental modal analysis, finite element modeling, model reduction and correlation tools in the MATLAB environment. A main brake squeal application serves a red line and is complemented by illustrations from other industries.

Benefits of Hilbert transform based methods of phase/frequency demodulation for order tracking and machine speed determination

In recent years it has become much more important to perform diagnostics on variable speed machines such as wind turbines. A very important tool for this is order tracking, to be able to express spectra in terms of shaft orders, where shaft harmonics are more localised. Despite what is often claimed, they are unlikely to be discrete components on an order scale, since order tracking removes  frequency modulation, but not amplitude modulation, causing the shaft related components to be smeared to some extent on an order scale. Even so, it is important for the phase/time curve used to resample the time signals at equal intervals of rotation angle to be as accurate as possible, and this can best be achieved by phase demodulation of a tacho signal using Hilbert transform techniques via the frequency domain. This is because information from a tacho signal is only available once per revolution, and interpolation by other means gives errors proportional to the spacing of the samples. By contrast, as long as the spectrum of the modulated carrier can be isolated by a window on the frequency scale, the true phase/time curve can be regenerated to any degree of resolution by increasing the sampling frequency of the resampled signal (similar to reconstructing a time signal from its FFT spectrum to any degree of resolution as long as the sampling theorem is obeyed).Accurate resampling is particularly important when transformations between the time and angle domains have to be made in both directions, and possibly several times. The most accurate measurements of angular velocity can also be made using these same principles, and this is also becoming an important diagnostic method, by detecting very small variations in speed (for example caused by bearing faults). It is also shown that the information on machine speed obtained by demodulating vibration response signals is not in general the same as that obtained from a tacho signal, and the small errors can be quantified. The tutorial explains the background for the above claims, with numerous examples.

Nonlinear Vibration Analysis of Modern Structures Using the NI2D Software: From Setup Preparation to Nonlinear Model Updating and Simulations

Modern structures and their subsystems are submitted to rigorous qualification and certification processes. In this context, the need for trustworthy finite element models is crucial. However, the growing occurrence of nonlinear structural phenomena makes the validation of numerical models more arduous, if not impossible, by using only linear analysis. Performing a complete identification of the nonlinearities and upgrading the model with nonlinear elements is therefore required.

This tutorial is intended to provide deep insights into the impact of nonlinearities in structural dynamics, and into the existing solutions to account for them. The first part will cover the different steps related to nonlinear test campaigns, from the construction of a nonlinear setup to the comprehensive nonlinear analysis of measurements. In the second part, nonlinear model creation and updating will be introduced, followed by nonlinear modal analysis and simulations. Rigorous theoretical and experimental approaches will be described in the tutorial, and demonstrations using the Nonlinear Identification to Design (NI2D) software will help attendees gain experience with the new concepts and tools.