Iemma U., Sciuto S., Diez M.

The paper deals with the application of an extension of the Karhunen-Loeve Decomposition (KLD) to the modal analysis of a non-homogeneous structure. Specifically, the methodology developed by the authors, and validated in the past only on the basis of computer simulations, has been here applied to the experimental analysis of a uniform steel beam, sensed with four accelerometersplaced in different configurations. Their signals, adequately conditioned, have been acquired by means of an automatic measuring system in order to make numeric data available for further post-processing. The dimension and weight of the sensors are such that their influence on the beam motion can not be neglected, thus imposing to consider the instrumented system as a non uniform vibrating structure. It can be shown that the application of the KLD to the time history of the elastic displacement, provides a set of eigenfunctions that correspond, in the limit for the observation time T tending to infinity, to the fundamental modes of the vibrating structure. In practical applications, T must be as long as a “good” statistical representation of the motion is ensured. This requirement is fulfilled if the fundamental mode with the lowest frequency present in the motion undergoes a sufficient number of periods during the acquisition time. One of the more appealing features of the method is that its statistical nature makes the results of the analysis independent of the excitation used to initiate the motion. The results obtained for the cantilever beam are in excellent agreement with the result of a FEM simulation. The fundamental frequencies are obtained by Fourier-transforming the projection of the time histories onto the KLD eigenfunctions. The resulting eigenfrequencies are in excellent agreement with the FEM simulation, for the first four fundamental modes of vibration. In addition, a preliminary estimate of the damping as a function of frequency is obtained using a novel methodology, based on the optimal matching of the time histories projections with an ideal damped oscillator.