Experimental dynamic substructuring using direct time-domain deconvolved impulse response functions

Abstract

The dynamics of systems can be analysed by combining the dynamics of its components. This method is generally know as dynamic substructuring. It allows for efficient computation of the dynamics of structures that would otherwise be to complex to determine. Most dynamic substructuring approaches use the frequency domain for the re-assembling of the subcomponents. Recently, a different implementation of the dynamic substructuring method has been introduced: impulse based substructuring (IBS). It uses impulse response function in the time-domain for representing the dynamics of the subcomponents, obtained by numerical models or experimental testing. Compared to the frequency domain methods, the impulse based substructuring scheme proves to be advantageous when analysing the high-frequency characteristics of a system. The high-frequency dynamics are excited when the system is subjected to blasts, shocks or impulsive loading. Due to the sensitivity of the impulse based substructure scheme, experimentally obtained impulse response functions can not be used for describing the dynamics of a subsystem. The focus of this thesis is developing a direct time-domain technique for determining the experimental impulse response. This is realised by introducing the inverse finite impulse response force filter, which operates independent of the output system response. This time-domain approach will avoid frequency domain induced errors, i.e. windowing, anti-aliasing and Fourier transforms, in the effort of determining a highly accurate impulse response functions. The quality of the time-domain acquired impulse response, as well as the measurement induced errors are tested on the impulse based substructuring scheme. The procedures are illustrated by application to an one-dimensional bar. The inverse force filter is successful in finding the experimental (averaged) impulse response. The accuracy of the filter depends on the length of the filter and the conditioning of the force auto correlation matrix. The eigenvalue decomposition of this matrix led to the formulation of a selection criteria between replicate measurements and a filtering operation. The inverse filter can also be defined by using a Fourier transform and its inverse. If both methods are compared, it is shown that the time-domain approach is less accurate and time efficient. The direct time-domain approach did not change the impulse response in such an extend that coupling by the impulse based substructuring scheme was possible. Since coupling between numerically simulated data is possible, measurement errors are introduced on the impulse response functions to test their sensitivity to the IBS scheme. It is observed that a small error on the exponential decay, of the perfect impulse response, directly resulted in uncoupled full system responses. This led to the identification of the modal parameters of the measurement to get rid of these amplitude errors, by means of the least squares complex exponential method. The perfect synthesised impulse response are successful in finding a coupled full system response. Experimental dynamic substructuring only finds the full coupled response if a clean synthesised impulse response function of the subcomponents is used. It can also be concluded that the inverse filter is not as accurate as its frequency domain counterpart. However, the inverse force filter will make deconvolution of small parts of the output response possible. This is desirable when testing lightly damped structures.