Monitoring crack growth through change of modal parameters
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Journal of Sound and Vibration (1995) 186(2), 325–343
MONITORING CRACK GROWTH THROUGH CHANGE OF MODAL PARAMETEngineering and Applied Science , Memorial University of Newfoundland , St John ’s , Newfoundland , Canada A 1B 3X 5 (Received 14 December 1993, and in final form 12 October 1994) Modal analysis was performed on a cantilever plate with a small crack, using finite element analysis. Modal parameters such as natural frequencies, magnitude of frequency response functions, displacement mode shapes and strain mode shapes were calculated against cracking in the plate. It was found that the surface crack in the structure will affect most of the modal parameters, such as the natural frequencies of the structure, amplitudes of the response and mode shapes. Some of the most sensitive parameters are the difference of the strain mode shapes and the local strain frequency response functions. By monitoring the changes in the local strain frequency response functions and the difference between the strain mode shapes, the location and severity of the crack that occurs in the structure can be determined. It was also observed from other parallel studies that the use of a proper and careful experimental procedure would eliminate the noise problems always present in strain gauge instrumentation.
Figure 1(a,b).
327
Figure 1(c,d).
performed and a reduction in natural frequencies and an increase in structural responses were reported. Gomes and Silva [2–4] conducted a series of studies using modal analysis for crack identification in simple structures. Modal tests of cantilever beams with fatigue cracks at different locations were performed for different crack depths. The influence of a lumped mass, which was attached to the structure (to simulate the end loads in structures), was also studied. The main modal parameter that was monitored was the natural frequencies of the vibrating beam. A series of non-dimensional curves and tables depicting the changes in natural frequencies for various depths of the crack, locations of the crack, and lumped mass were presented. Use of these tables and figures would lead to identification of the probable depth and location of the crack in any beam. Richardson and Mannen [5] developed modal sensitivity functions for the location of structure faults due to a change of mass, stiffness and/or damping of structure components. Most researchers have stated that damage in structures tends to reduce the natural frequencies; consequently, with knowledge of the changes in natural frequencies it becomes possible to determine the extent of cracks or damage in a structure. However, it is hard to determine the location of the crack by this procedure, since cracks at two different locations, associated with certain crack lengths or depths, may cause the same amount of frequency shift at certain modes. However, Hearn et al . [6] have pointed out in their paper that the magnitudes of the changes for different natural frequencies are a function of the severity and
325
0022–460X/95/370325+19 $12.00/0 7 1995 Academic Press Limited
326
. . . .
analysis proved to be ineffective, since the researchers considered only the frequency shifts, and these shifts could be caused by a number of factors such as cracking and damage, erosion and strength degradation of the foundation, addition of extraneous mass to the sub/superstructure, etc. Recent studies in modal analysis have been focused on the total dynamic behaviour. The physical properties of any structure can be expressed in term of its mass, stiffness and damping. Any damage that occurs in the structure will cause changes in these physical properties; and these changes will be reflected in change in the dynamic characteristics of the structure, such as the natural frequencies, displacements, strains/stresses, mode shapes and damping, which can be obtained from the frequency response functions (FRFs). This study investigates the sensitivities of the dynamic characteristics of any structure to crack development so as to develop a suitable technique to monitor and detect cracks or damage in structures.
2. SURVEY OF PERTINENT EARLIER INVESTIGATIONS
Shahrivar et al . [1] determined the natural frequency shifts in an offshore structure due to the presence of damages in structure elements. Modal testing of an offshore framed platform model, with grossly cracked structural members (severed members), was
7 1995 Academic Press Limited
1. INTRODUCTION
Structures under repeated harmonic/random loadings inevitably develop cracks. For instance, offshore structures are subjected to repeated loadings due to ocean waves which impose a large number of cyclic stresses; under these varying cyclic stresses fatigue cracks develop at critical welded junctions of offshore structures. Therefore the prediction, detection and monitoring of cracks in structures has been the subject of intensive investigation during recent years. Its importance is shown in the strict guidelines enforced on the design of structures and structural components, as well as on the maintenance and repair carried out on in -situ structures for maximum effectiveness at minimum cost. Many theoretical and experimental studies of the behaviour of structures with cracks have been carried out to develop a feasible methodoogy. Thousands of theoretical and experimental studies have been carried out in the allied area of fracture mechanics. Meanwhile, many techniques have been developed to quantify cracking in structures, such as acoustic emission, magnetic particle inspection, dye penetrant, alternating/direct current field measurement, eddy current, laser interferometry, ultrasonics and modal testing. In recent years, Non-Destructive Evaluation (NDE) has gained a greater attention for monitoring and detecting cracks developed in operating structures, and several techniques have been developed, as mentioned before. Each of these methods has its own advantages and disadvantages. New techniques are being developed to meet the new requirements of structures in increasingly severe environments. Among these newly emerging techniques, the modal analysis and testing procedure is being explored by many researchers to determine whether it can be used as an efficient technique for non-destructive examination, especially if the modal strains around the critical zones could be monitored. Earlier studies on modal
MONITORING CRACK GROWTH THROUGH CHANGE OF MODAL PARAMETEngineering and Applied Science , Memorial University of Newfoundland , St John ’s , Newfoundland , Canada A 1B 3X 5 (Received 14 December 1993, and in final form 12 October 1994) Modal analysis was performed on a cantilever plate with a small crack, using finite element analysis. Modal parameters such as natural frequencies, magnitude of frequency response functions, displacement mode shapes and strain mode shapes were calculated against cracking in the plate. It was found that the surface crack in the structure will affect most of the modal parameters, such as the natural frequencies of the structure, amplitudes of the response and mode shapes. Some of the most sensitive parameters are the difference of the strain mode shapes and the local strain frequency response functions. By monitoring the changes in the local strain frequency response functions and the difference between the strain mode shapes, the location and severity of the crack that occurs in the structure can be determined. It was also observed from other parallel studies that the use of a proper and careful experimental procedure would eliminate the noise problems always present in strain gauge instrumentation.
Figure 1(a,b).
327
Figure 1(c,d).
performed and a reduction in natural frequencies and an increase in structural responses were reported. Gomes and Silva [2–4] conducted a series of studies using modal analysis for crack identification in simple structures. Modal tests of cantilever beams with fatigue cracks at different locations were performed for different crack depths. The influence of a lumped mass, which was attached to the structure (to simulate the end loads in structures), was also studied. The main modal parameter that was monitored was the natural frequencies of the vibrating beam. A series of non-dimensional curves and tables depicting the changes in natural frequencies for various depths of the crack, locations of the crack, and lumped mass were presented. Use of these tables and figures would lead to identification of the probable depth and location of the crack in any beam. Richardson and Mannen [5] developed modal sensitivity functions for the location of structure faults due to a change of mass, stiffness and/or damping of structure components. Most researchers have stated that damage in structures tends to reduce the natural frequencies; consequently, with knowledge of the changes in natural frequencies it becomes possible to determine the extent of cracks or damage in a structure. However, it is hard to determine the location of the crack by this procedure, since cracks at two different locations, associated with certain crack lengths or depths, may cause the same amount of frequency shift at certain modes. However, Hearn et al . [6] have pointed out in their paper that the magnitudes of the changes for different natural frequencies are a function of the severity and
325
0022–460X/95/370325+19 $12.00/0 7 1995 Academic Press Limited
326
. . . .
analysis proved to be ineffective, since the researchers considered only the frequency shifts, and these shifts could be caused by a number of factors such as cracking and damage, erosion and strength degradation of the foundation, addition of extraneous mass to the sub/superstructure, etc. Recent studies in modal analysis have been focused on the total dynamic behaviour. The physical properties of any structure can be expressed in term of its mass, stiffness and damping. Any damage that occurs in the structure will cause changes in these physical properties; and these changes will be reflected in change in the dynamic characteristics of the structure, such as the natural frequencies, displacements, strains/stresses, mode shapes and damping, which can be obtained from the frequency response functions (FRFs). This study investigates the sensitivities of the dynamic characteristics of any structure to crack development so as to develop a suitable technique to monitor and detect cracks or damage in structures.
2. SURVEY OF PERTINENT EARLIER INVESTIGATIONS
Shahrivar et al . [1] determined the natural frequency shifts in an offshore structure due to the presence of damages in structure elements. Modal testing of an offshore framed platform model, with grossly cracked structural members (severed members), was
7 1995 Academic Press Limited
1. INTRODUCTION
Structures under repeated harmonic/random loadings inevitably develop cracks. For instance, offshore structures are subjected to repeated loadings due to ocean waves which impose a large number of cyclic stresses; under these varying cyclic stresses fatigue cracks develop at critical welded junctions of offshore structures. Therefore the prediction, detection and monitoring of cracks in structures has been the subject of intensive investigation during recent years. Its importance is shown in the strict guidelines enforced on the design of structures and structural components, as well as on the maintenance and repair carried out on in -situ structures for maximum effectiveness at minimum cost. Many theoretical and experimental studies of the behaviour of structures with cracks have been carried out to develop a feasible methodoogy. Thousands of theoretical and experimental studies have been carried out in the allied area of fracture mechanics. Meanwhile, many techniques have been developed to quantify cracking in structures, such as acoustic emission, magnetic particle inspection, dye penetrant, alternating/direct current field measurement, eddy current, laser interferometry, ultrasonics and modal testing. In recent years, Non-Destructive Evaluation (NDE) has gained a greater attention for monitoring and detecting cracks developed in operating structures, and several techniques have been developed, as mentioned before. Each of these methods has its own advantages and disadvantages. New techniques are being developed to meet the new requirements of structures in increasingly severe environments. Among these newly emerging techniques, the modal analysis and testing procedure is being explored by many researchers to determine whether it can be used as an efficient technique for non-destructive examination, especially if the modal strains around the critical zones could be monitored. Earlier studies on modal