Longitudinal wave propagation. Part II—Analysis of crack influence

Computers & Structures, 2002

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. : S 0 0 4 5 -7 9 4 9 ( 0 2 ) 0 0 2 1 9 -5

Finite Elements in Analysis and Design, 2004

This paper presents the method of analysis of the wave propagation process in cracked plates. For modelling the plate new type of ÿnite spectral plate element with a crack was elaborated. It was assumed that the crack having an arbitrary length, depth and location was parallel to one side of the plate. Elastic behaviour of the plate at the crack location was considered as a line spring with a varying sti ness along the crack length.

International Journal of Non-Linear Mechanics

In this paper we consider the problem of identifying an open crack in a longitudinally vibrating rod with smooth variable profile by minimal eigenfrequency data. The crack is assumed to be open during vibration and it is modelled by an elastic spring acting along the beam axis. Most, if not all, the results available in the literature for this inverse problem refer to ideal end conditions, that is the rod is either under free or supported end conditions. As an example of almost optimal result, it is known that the knowledge of the fundamental (positive) natural frequency of the rod under free-free and cantilever end conditions allows for the unique determination of the crack, without any restriction on the damage severity. In this paper we show that the analysis of the analogous crack identification problem for rods under elastically restrained end conditions leads to different results and that, in general, the knowledge of the fundamental frequency belonging to two spectra associated to different end conditions is not sufficient for the uniqueness of the solution. The method we used to solve the inverse problem is of constructive type and it is based on general properties of

Engineering Fracture Mechanics, 2010

ABSTRACT In this study, the possibility of continuously monitoring load-carrying cables in bridges is considered. A sending/receiving transducer is used to generate an ultrasonic, longitudinal, elastic wave through the cable. The interaction between the L(0,1)-wave and vertical cracks in a single rod is investigated using the Waveguide-FE-Method to predict the reflection and transmission coefficients. Moreover, this work analyzes how the elastic energy of a propagating wave is distributed between adjacent rods via friction. An energy-based model is developed to approximate the coupling behavior in a two-rod system. Finally, the numerical predictions are verified by experimental data.

Journal of Sound and Vibration, 2015

The basic problem in structural diagnostics via dynamic methods consists in determining the position and severity of a single open crack in a beam from the knowledge of a pair of resonant or antiresonant frequencies. A well-established theory is available for longitudinally vibrating uniform beams when the severity of the crack is small. In this paper we fill the gap present in the literature by showing that the results of the linearized theory for slight damage can be extended to a crack with any level of severity.

Science and Engineering of Composite Materials, 2004

A spectral finite element model for analysis of flexural-shear coupled wave propagation in a multilayer composite beam with a transverse open and not propagating crack is presented. The concept of obtaining the exact spectral element dynamic stiffness matrix is discussed. Computation is performed in the frequency domain at FFT sampling points over a broad frequency band. Post processing of the response is made in the time domain, which is suitable for structural diagnostics and broad-band wave propagation problems. Implemented numerical examples illustrate the influence of crack on wave propagation in cantilever multilayer laminated composite beams. INTRODUCTION Composite materials play an increasing role in many engineering applications. High performance, strength, stiffness and low weight are the attractive factors which increase the use of these materials in aerospace, automobile, marine and rail industries. One of the major concerns associated with composites is their susceptibility to damage, which may occur during manufacture, service or maintenance. Among others, delamination, matrix and fibre cracking are the most common damages occurring in composite materials. Although such damages are barely visible, they can severely degrade the mechanical properties and the load carrying capability of the structure. Any growth of this damage can lead to fracture of the material. Most of the structural health monitoring methods can be classified into model-based and signal-based approaches. The former utilises structural physical parameters for damage detection and is rather related to modelling and identification problems; any change of structural physical parameters can indicate damage /I/. The signal-based approach uses different vibration, strain, acoustical and ultrasonic signals for damage detection and is related to signal processing. It is usually based on a relationship between a structure condition and a damage symptom or feature, where the problem is to find symptoms which are sensitive to damage and damage evolution. The paper is devoted to utilizing wave propagation as an efficient tool for damage detection in composite structures. Many numerical methods are applied for wave propagation modelling. The most efficient and convenient among them is spectral element method (SEM) 121. The SEM is based on exact solution to governing Partial Differential Equations (PDE) in the frequency domain /3/. This exact solution is used as interpolating function for spectral element formulation. The use of an exact solution in the element formulation ensures exact mass and stiffness distribution. As a result, the element directly yields the exact dynamic 55 Unauthenticated Download Date | 7/8/16 12:31 AM Vol. 11, No. 1, 2004 Flexural-Shear Wave Propagation in Cracked Composite Beam Unauthenticated Download Date | 7/8/16 12:31 AM

Journal of Vibration and Control, 2014

It has been known for a long time that the problem of identifying two small cracks in a simply supported beam from the first three natural frequencies can be analytically formulated and solved if the two cracks have equal severity. In this paper we extend this result to the case of cracks with different severity. Each crack is simulated by a rotational elastic spring and the inverse problem is solved in terms of the damage induced changes in the first four natural frequencies.

International Journal of Solids and Structures, 2015

We consider the inverse problem of identifying a single open crack in a longitudinally vibrating rod having non-uniform smooth profile. Without any a priori assumption on the smallness of the damage and assuming that the rod profile is symmetric with respect to the mid-point of the rod axis, we present a constructive diagnostic algorithm from minimal frequency data. We show that the crack can be uniquely identified, up to a symmetric position, from the first two positive natural frequencies of the rod under free-free end conditions. We also show that the non-uniqueness of the damage location can be removed by using as data the first positive resonant frequency of the free-free rod and the first antiresonant frequency of the driving-point frequency response evaluated at one end of the rod. The results of numerical simulations and of applications of the method to experimental data agree well with the theory.

Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, Civil Infrastructure, and Transportation XII, 2018

Structural health monitoring (SHM) and nondestructive evaluation (NDE) deals with the nondestructive inspection of defects, corrosion, leaks in engineering structures by using ultrasonic guided waves. In the past, simplistic structures were often considered for analyzing the guided wave interaction with the defects. In this study, we focused on more realistic and relatively complicated structure for detecting any defect by using a non-contact sensing approach. A plate with a stiffener was considered for analyzing the guided wave interactions. Piezoelectric wafer active transducers were used to produce excitation in the structures. The excitation generated the multimodal guided waves (aka Lamb waves) that propagate in the plate with stiffener. The presence of stiffener in the plate generated scattered waves. The direct wave and the additional scattered waves from the stiffener were experimentally recorded and studied. These waves were considered as a pristine case in this research. A fine horizontal semi-circular crack was manufactured by using electric discharge machining in the same stiffener. The presence of crack in the stiffener produces additional scattered waves as well as trapped waves. These scattered waves and trapped wave modes from the cracked stiffener were experimentally measured by using a scanning laser Doppler vibrometer (SLDV). These waves were analyzed and compared with that from the pristine case. The analyses suggested that both size and shape of the horizontal crack may be predicted from the pattern of the scattered waves. Different features (reflection, transmission, and mode-conversion) of the scattered wave signals are analyzed. We found direct transmission feature for incident A0 wave mode and modeconversion feature for incident S0 mode are most suitable for detecting the crack in the stiffener. The reflection feature may give a better idea of sizing the crack.

Computers & Structures, 2004

The wave propagation model investigated herein is based on the known fact that material discontinuities affect the propagation of elastic waves in solids. The change in certain material characteristics, such as a local change in stiffness or inertia caused by a crack or the presence of material damage, will affect the propagation of transmitted elastic waves and will modify the received signal. Wave frequencies associated with the highest detection sensitivity depend, among other things, on the type of structure, the type of material, and the type of damage. This paper presents a method of wave propagation, which can be further used to detect small delaminations in beam-like structures. The considered beam is modelled by spectral finite elements.