Detection of debonding in adhesive joints using Lamb wave propagation

Adhesively bonded joints are widely used in many branches of industry. Mechanical degradation of this type of connections does not have significant symptoms that can be noticed during visual assessment, so non-destructive testing becomes a very important issue. The paper deals with experimental investigations of adhesively bonded steel plates with different defects. Five samples (an intact one and four with damages in the form of partial debonding) were prepared. The inspection was conducted with the use of guided wave propagation method. Lamb waves were excited at one point of the sample, whereas the out-of-plane velocity signals were recorded in a number of points spread over the area of overlap. The processing of signals consisted of calculations of weighted root mean square (WRMS). The results of the analysis showed that the WRMS maps allow for identification and determination of size and shape of debonding areas

Methods of small parameter in mathematical biology

This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant and preserves the salient features of the dynamics. The aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools described allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value.   The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques.   Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and  graduate students in appled and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis

Analiza numeryczna i doświadczalna propagacji pola elektromagnetycznego w badaniach metodą georadarową

This paper presents experimental tests by using the GPR method and numerical analysis of electromagnetic field propagation. The object of the experimental research was a ground floor structure. An antenna of frequency of emitted waves equal to 2 GHz was used for measurements. The paper also describes the numerical modelling of electromagnetic field with the use of the finite difference time domain method. Results of propagation of electromagnetic waves in a one-dimensional reinforced concrete specimen were presented.W pracy przedstawiono badania doświadczalne metodą georadarową oraz analizę numeryczną propagacji pola elektromagnetycznego. Przedmiotem badań eksperymentalnych była konstrukcja podłogi. Pomiary wykonano za pomocą georadaru o częstotliwości emitowanej fali równej 2 GHz. W artykule opisano także sposób numerycznego modelowania elektromagnetycznego pola falowego za pomocą metody różnic skończonych w dziedzinie czasu. Przedstawiono wyniki propagacji fali elektromagnetycznej w próbce żelbetowej dla przypadku jednowymiarowego

Detection of debonding in adhesive joints using Lamb wave propagation

Adhesively bonded joints are widely used in many branches of industry. Mechanical degradation of this type of connections does not have significant symptoms that can be noticed during visual assessment, so non-destructive testing becomes a very important issue. The paper deals with experimental investigations of adhesively bonded steel plates with different defects. Five samples (an intact one and four with damages in the form of partial debonding) were prepared. The inspection was conducted with the use of guided wave propagation method. Lamb waves were excited at one point of the sample, whereas the out-of-plane velocity signals were recorded in a number of points spread over the area of overlap. The processing of signals consisted of calculations of weighted root mean square (WRMS). The results of the analysis showed that the WRMS maps allow for identification and determination of size and shape of debonding areas

Semigroups of Operators : Theory and Applications

Many results, both from semigroup theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semigroup theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and, in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful

Damage Imaging in Lamb Wave-Based Inspection of Adhesive Joints

Adhesive bonding has become increasingly important in many industries. Non-destructive inspection of adhesive joints is essential for the condition assessment and maintenance of a structure containing such joints. The aim of this paper was the experimental investigation of the damage identification of a single lap adhesive joint of metal plate-like structures. Nine joints with different defects in the form of partial debonding were considered. The inspection was based on ultrasonic guided wave propagation. The Lamb waves were excited at one point of the analyzed specimen by means of a piezoelectric actuator, while the guided wave field was measured with the use of a laser vibrometer. For damage imaging, the recorded out-of-plane vibrations were processed by means of the weighted root mean square (WRMS). The influence of different WRMS parameters (i.e., the time window and weighting factor), as well as excitation frequencies, were analyzed using statistical analysis. The results showed that two-dimensional representations of WRMS values allowed for the identification of the presence of actual defects in the adhesive film and determined their geometry