A numerical-experimental study on damaged beams dynamics

Abstract

Article citation info: IntroductionIn many contemporary structures various types of defects can appear leading to significant reduction of the element rigidity and changing its overall mechanical behaviour. A special challenge is detection and localization of hidden defects, which can have many forms depending on the scale of the problem, eg. dislocations, voids or inclusions in microscale [43,49,44,3] to macroscopic defects, such as delamination in laminated composites [31] or welds in metallic materials [53,50]. The current work is focused on testing the applicability of dynamic vibration-based, as well as the space analysis methods to defect detection and localization in 1D (beam) structures. The vibration-based methods have been widely used in the plates and beams dynamics. For example, Manoach et al. [25,26,27,24,48] analysed the frequencies and modes of free vibrations in order to identify damage in beam and plates. The most interesting aspect of these papers was introduction of the so-called Damage Index exploiting the information given by the Poincaré maps [19]. The authors of the current study aimed at testing other dynamical methods towards detection and localization of defects in structures, which led them to reach for time series analysis.Experimental time series, especially nonlinear, can be analyzed by means of the method of delay coordinates, which allows to reconstruct a phase space and Poincaré section. This procedure is precisely described in [2,32] and can be applied for analysis of experimental signals obtained from different kinds of real processes [12,5] and numerical simulations [40]. For instance, the delay coordinate technique is used for researching dynamics of robot joints [47] and to analyse nonlinear system with dry friction [40]. Interesting contribution in the field of phase space reconstruction is presented in [7,8,36] in which the method of delay coordinates is employed for experimental and numerically generated signals, also with noise. Another example can be an impact and a self-excited oscillator with CoulombAmontons friction [13].On the basis of delay coordinates method, a recurrence plot technique is introduced to analyse linear or non-linear stationary and also non-stationary time series [30]. The formal concept of recurrences was introduced by Henri Poincaré in his seminal work from 1890 [37], for which he won a prize sponsored by King Oscar II of Sweden and Norway [30]. Therein, Poincaré did not only discover the homoclinic tangl which lies at the root of the chaotic behaviour of orbits, but he also introduced (as a by-product) the concept of recurrences in conservative systems. Even though much mathematical work was carried out in the following years, Poincaré's pioneering work and his discovery of recurrence had to wait for more than 70 years for the development of fast and efficient computers to be exploited numerically. The use of powerful computers boosted chaos theory and allowed to study new and exciting systems. Some of the tedious computations needed to use the c...

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