Analysis of longitudinal wave propagation in a cracked rod by the spectral element method Magdalena Palacz a, * , Marek Krawczuk b,1 a Institute of Fluid Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gdansk, Poland b Department of Technical Sciences, University of Warmia and Mazury, Oczapowskiego 22, 10-736 Olsztyn, Poland Received 13 December 2001; accepted 26 July 2002 Abstract The aim of this paper is to introduce a new finite spectral element of a cracked rod for damage detection. The proposed approach deals with the spectral analysis method as a means of solving the wave propagation problems in structures. The change of the wave propagation process due to a crack appearance, is examined by comparing the differences between the responses from damaged and undamaged rods. The influence of the crack growth for the wave propagation is also examined. The rod element was excited with different signals in order to determine the influence of the nature of the signal for the wave propagation process. The differences in the propagating waves allow to indicate the crack location in a very precise way. This fact is very promising for the future work on the damage detection field. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Wave propagation; Cracked rod; Spectral analysis 1. Introduction Infrastructure health monitoring and damage detec- tion has received a considerable amount of interest over the last few decades [1–3]. Previous non-destructive ap- proaches to evaluate the integrity of structures typically involved some form of human interaction. Recent ad- vances in smart materials and structures technology has resulted in a renewed interest in developing advanced self-diagnostic capability for assessing the state of a structure without any human interaction. The goal is to reduce human interaction while at the same time mon- itor the integrity of the structure. With this goal in mind, many researchers have made significant strides in de- veloping damage detection methods for structures based on traditional modal analysis techniques. These tech- niques are often well suited for structures, which can be modelled by discrete lumped-parameter elements where the presence of damage leads to some low frequency change in the global behaviour of the system [4–7]. On the other hand small defects such as cracks are obscured by modal approaches because such phenomena are high frequency effects which are not easily discovered by ex- amining changes in modal mass, stiffness or damping parameters. This is because at high frequency, modal structural models are subjected to uncertainty. Increas- ing the order of the discrete model can reduce this un- certainty; however, this increases the computational effort of modal-based damage detection schemes. On the other hand, structural models based on wave propaga- tion, are well suited for detecting small defects since they are sensitive to changes in local dynamic impedance [8,9]. Over the years many analytical techniques have been developed for treating wave propagation problems. Central among these is the method of Fourier synthesis (or spectral analysis). The significance of the spectral approach to waves is that once the signal is characterised at one space position, then it is known at all positions, Computers and Structures 80 (2002) 1809–1816 www.elsevier.com/locate/compstruc * Corresponding author. Fax: +48-58-341-61-44. E-mail addresses: mpal@imp.gda.pl (M. Palacz), mk@imp.gda.pl (M. Krawczuk). 1 Fax: +48-89-523-32-55. 0045-7949/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0045-7949(02)00219-5