This helps to avoid the Runge phenomenon, that is, large oscillations of approximating polynomials near the edges FEs. A characteristic of TD-SFEM is a non-uniform distribution of nodes within SFEs, which results from the distance between the roots of certain polynomials. These functions describe the distribution of the analysed physical properties inside finite elements (FEs) and at its boundaries. The property of FEM is that for each simple geometric object, specific points (called nodes) with certain approximating functions (called shape functions or node functions) are determined. TD-SFEM is a computational technique that combines the properties of the polynomial approximation of spectral methods and the approach to the discretisation of the analysed area inherent in the finite element method (FEM). This additionally improves the numerical performance of the method.įor numerical modelling, TD-SFEM has been chosen. Moreover, it is well known that thanks to the orthogonality of high-order approximation polynomials used in TD-SFEM, the diagonal forms of the inertia matrix are obtained. This is especially important in the context of numerical calculations related to modelling wave propagation. The main advantage of TD-SFEM is a more precise representation of high frequency signals than in the case of the classical Finite Element Method (FEM). However, the most versatile method for modelling wave propagation has been the Time-domain Spectral Finite Element Method (TD-SFEM). Numerical or grid-based methods have found a wide range of applications to solve elastic wave propagation problems arising in seismology, medical ultrasound and non-destructive evaluation or even textile industry. For example, analytical models for modelling wave propagation in plate elements made out of various composite materials have been proposed in. Various approaches to the proper modelling of complicated wave propagation phenomena can be found in the literature. On the other hand, the numerical sensitivity is limited to the proper mathematical model used for solutions. The numerical analysis has been carried out by the use of the Time-domain Spectral Finite Element Method (TD-SFEM), whereas the experimental part has been based on the measurement performed by 1-D Laser Doppler Scanning Vibrometery (LDSV). This paper discusses the results of research carried out by the authors in this regard both numerically and experimentally. Hence, a question arises about whether it is possible to shorten the required measurement time without affecting the sensitivity of the diagnostic method used. Diagnostic methods based on the elastic wave propagation phenomenon are becoming more and more popular, therefore it is worth focusing on the improvement of the efficiency of these methods. Recently, methods based on the analysis of changes in dynamic parameters of structures, that is, frequencies or mode shapes of natural vibrations, as well as changes in propagating elastic waves, have been developed at the highest rate. There are many methods of damage detection, in which changes in various parameters caused by the presence of damage are analysed. Damage detection in structural components, especially in mechanical engineering, is an important element of engineering practice.
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