Detection of multiple cracks using frequency measurements

Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements

Detection and localisation of multiple cracks in a shaft system: An experimental investigation

Ultrasonic vibrations in cracked structures generate heat at the location of defects mainly due to frictional rubbing and viscoelastic losses at the defects. Vibrothermography is an effective nondestructive evaluation method which uses infrared imaging (IR) techniques to locate defects such as cracks and delaminations by detecting the heat generated at the defects. In this paper a coupled thermo-electro-mechanical analysis with the use of implicit finite element method was used to simulate a low power (10 W) piezoceramic-based ultrasonic actuator and the corresponding heat generation in a metallic plate with multiple surface cracks. Numerical results show that the finite element software Abaqus can be used to simultaneously model the electrical properties of the actuator, the ultrasonic waves propagating within the plate, as well as the thermal properties of the plate. Obtained numerical results demonstrate the ability of these low power transducers in detecting multiple cracks in the simulated aluminum plate. The validity of the numerical simulations was verified through experimental studies on a physical aluminum plate with multiple surface cracks while the same low power piezoceramic stack actuator was used to excite the plate and generate heat at the cracks. An excellent qualitative agreement exists between the experimental results and the numerical simulation’s results.

Structural damage identification using static test data and changes in frequencies

Detection of Multiple Cracks on a Partially Obstructed Plate Following the Bayesian Approach

Most of the rotating machines used in process industries or in manufacturing plant need maintenance and repair. However, failure of just one of these machines can disturb an entire process with losses in terms of production, manpower, and equipment repair or replacement. Also failure of a single machine component in process industries like petrochemicals or power stations can result in the loss of millions of rupees per down time hour. These facts together with higher costs for new equipment have placed increased demand on plant maintenance to keep existing equipment operating efficiently with higher availability. A number of non-destructive crack detection techniques have been developed, such as ultrasonic testing, X-ray technique, magnetic particle method etc. Every method has some advantages and disadvantages. In recent years, ultrasonic testing has gained greater attention for monitoring the cracks in structures and machine components. Most of these methods are very laborious and time consuming, in the case of larger components like bridges, long pipe lines, railway tracks etc. These inconveniences can be avoided by the use of vibration monitoring technique such as model analysis. Therefore the development of vibration monitoring techniques has received increasing attention in recent years. Damage in structure alters its dynamic characteristics. The change is characterized by a change in model parameters i.e. model frequencies, model damping values and mode shapes associated with each model frequencies. Changes also occur in some of the structural parameters like mass, damping, stiffness and flexibility matrices of structure. Thus a vibration technique can be suitably used as a nondestructive test for crack detection of components to be tested. In this paper, theoretical and experimental analysis of a vibrating cantilever beam with a crack is carried out. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of natural frequencies, which are global parameter and can be easily measured from any point on the structure. In theoretical analysis the crack is simulated by an equivalent spring, connecting the two segments of the beam. Analysis of this approximate model results in algebraic equation, which relates the natural frequencies of the beam, and crack location. Also the relationship between the natural frequencies, crack location and crack size has also been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies are sufficient. The computation of natural frequencies of uncracked and cracked beam is facilitated by a finite element method package. This database is to be utilized in an analytical method to address the inverse problem to identify the crack location and crack size.

A dynamic mesh-refinement method (DMRM) of multiple cracks identification is presented, which is based on the relationship of natural frequency change ratios with crack parameters in a beam. The beam is first divided into a coare mesh and the crack is represented by a rotational spring, and expressions relating changes in natural frequencies and the damage index matrix are formulated via an influence matrix. The damage index matrix can be solved by the resulting system of linear algebraic equations. The elements corresponding to the damage indexes with positive values are predicted to contain the crack. Then, these damage elements are refined with the successive subdivision method. The influence matrix is reconstructed through integrating a new subdomain of the damage elements. The new damage index matrix for the refinement meh can focus the crack on the refinement element. In this way, elements are gradually refined until the desired element size is found. The final refinement result indicates the crack location. In each tiny damage element, the spring crack model can be used to quantify the size of the descrete crack. Numerical examples are proposed to demonstrate the effectiveness of the presented method.

In this paper, we discuss the dynamics of beams with multiple delaminations. The objective of the study is to use the dynamic response of the delaminated beams in health monitoring of composite structures. As a first step, we present experimental results on the vibrations of a cantilever beam with multiple delaminations. These experiments are conducted by exciting the beam with piezoelectric actuators. The response is detected by using a high-speed video camera to study the existence of delamination opening modes in a beam with multiple delaminations. Then, an analysis of natural frequencies and mode shapes, for a delaminated beam, is presented by using analytical techniques. The measured dynamic responses of the beam with multiple delaminations are also presented. The experimentally detected nonlinear response is discussed. Introduction Delaminations or interlayer cracks and impact damages are typical defects observed in composite structures. The presence of these defects changes the dynamic characteristics of the structure . Some of the specific changes in the observed dynamic characteristics include changes in natural frequencies, changes in the mode shapes and changes in damping ratios. These changes can be used to identify the existence, location and magnitude of a delamination or an impact damage, before they can grow to their critical sizes. Studies, to date, are concerned with the dynamics of beams and plates with a single delamination. In this paper, we specifically discuss the structural dynamics of a beam with multiple delaminations. This information can be used to develop health-monitoring techniques for composite beams with multiple delaminations. In an earlier paper, Luo and Hanagud studied the effects of defects, like saw-cuts, impact damage and delamination, on the structural dynamic characteristics of composite beams. They have shown that perturbations in natural frequencies and modes of a beam, due to defects, can be used for health monitoring of structures. In particular, it has been shown that an integral equation that considers perturbations in curvature modes and natural frequencies can be very effectively used to detect local defects. To distinguish delaminations from other types of monitored (identified) defects Luo and Hanagud have discussed nonlinear effects like superharmonic response in the dynamic response of a harmonically excited delaminated beam. They considered only a single delamination. In this paper we study beams with multiple delaminations. More specifically, we discuss dynamic response and the changes in natural frequencies, mode shapes due to multiple delaminations in a composite beam. One of the earliest models for vibration analysis of composite beams with delaminations was proposed by Ramkumar et al. This model simply used four Timoshenko beams connected at the delamination edges to model a composite beam with one throughwidth delamination. The predicted frequencies, based on this model, were consistently lower than the results of experimental measurements. Wang et al. improved the analytical solution by including coupling between flexural and axial vibrations of the delaminated sublaminates. Using an isotropic beam with splits and the classical beam model, they found that the calculated natural frequencies were closer to experimental results. With similar considerations, Nagesh Gummadi and Hanagud formulated a finite element solution for arbitrary composite beams. In the finite element models, they considered a classical composite beam model as well as the beam model with high order shear deformations. Mujumdar and Suryanarayan have proposed a model which imposed a constraint between the delaminated sublaminates to force them to have the same flexural displacement. This model was unable to * Ph.D. Student, School of Aerospace Engineering † Professor, School of Aerospace Engineering, AIAA Member Copyright © 1999 The American Institute of Aeronautics and Astronautics Inc. All rights reserved

Based on the Bernoulli–Euler theory, the vibration characteristics of a clamped-elastic pinned beam under the elastic constraint and the compressive axial loads are derived and verified by finite element method. The results of examples show that the natural frequency of the beam decreases with loads increase and the frequency increases with the increase of the elastic constraint stiffness. When the constraint stiffness increases from 104 to 108 N/m, the first-order natural frequency becomes 4.24 times, the second-order natural frequency becomes 2.19 times, and the third-order natural frequency becomes 1.57 times; when the constraint is weak, the loads change is mainly reflected in the first mode shape. When the constraint stiffness is 104 N/m, the first-order natural frequency decreases by 20%, the second-order modal natural frequency changes by 3%, and the third-order natural frequency changes by less than 1%. The range of the elastic constraints with significant changes in the natural frequencies of the higher-order modes is larger. When the first-order frequency is taken to 100EI/l3, the change tends to be flat, the second-order frequency is about five times that of the first-order, and the range of the third-order frequency is 15 times or more.

Securing the structural safety of blades has become crucial, owing to the increasing size and weight of blades resulting from the recent development of large wind turbines. Composites are primarily used for blade manufacturing because of their high specific strength and specific stiffness. However, in composite blades, joints may experience fractures from the loads generated during wind turbine operation, leading to deformation caused by changes in structural stiffness. In this study, 7132 debonding damage data, classified by damage type, position, and size, were selected to predict debonding damage based on natural frequency. The change in the natural frequency caused by debonding damage was acquired through finite element (FE) modeling and modal analysis. Synchronization between the FE analysis model and manufactured blades was achieved through modal testing and data analysis. Finally, the relationship between debonding damage and the change in natural frequency was examined using artificial neural network techniques.

Based on the measured vibration information, a method for detecting reduction in stiffness parameters of a structure using generalized flexibility matrix and changes in natural frequencies is presented in this paper. For incomplete measured data of the first mode shape, dynamic expansion of mode shape is introduced. The generalized flexibility matrix is approximately constructed by using the measured first frequency and the extended mode shape only, and it is further used to detect the possible damaged elements. An iterative algorithm using the changes of the first several natural frequencies only is subsequently used to update the damage extent of these possible damaged elements, while the number of damage-extent parameters to be determined in the algorithm is remarkably reduced. Finally, two numerical examples concerning a two-span beam and a two-story frame are used to illustrate the effectiveness of the proposed method.

The presence of faults is common in engineering composite structures. Precise detection of faults prior to failure has been the focal point for researchers working in this domain. Detection of damage from the modal characteristics is an age-old promising technique besides the artificial intelligence techniques such as neural network (NN), Artificial neural network (ANN), recurrent neural network (RNN), and particle swarm optimization (PSO) methods. However, multiple detection techniques combined can give better results. In this regard, recurrent neural networks (RNN) and modified particle swarm optimization (mPSO) are combined to detect damages in a glass fiber reinforced polymer (GFRP) composite cantilever beam. The proposed hybrid model consists of two stages; indices of relative natural frequencies applied to locate crack parameters (position and severity) by recurrent neural network technique and optimization of the results (position and severity) by mPSO. The results illustrate this method can be implemented to predict multiple transverse cracks and their parameters in a composite beam, manifested in the change of natural frequencies where the error is limited to 0.97% only.

In order to clarify the influence of water on the natural vibration of bridge with complex piers, based on a continuous beam with 4-column pier, the numerical analysis model is established. Single column circular pier is taken to discuss the range of waters. Then the influences of water on the natural vibration are analyzed. The research shows that waters reduce the natural frequency. When waters area width is less than 10 m, the natural frequency of the pier decreases. And the first-order longitudinal bending frequency is reduced by 3.36%. When waters area width is more than 10 m, the vibration frequencies tend to be stable gradually. Therefore, the waters 10 m can be regarded as an infinite boundary. The natural frequencies of single column pier and 4-column pier decrease with the increase of water depth. When the water depth is less than 10 m, the changes of natural frequency of the first four orders of single column pier are relatively small, and the changes of 5–10 order natural frequency are large. The maximum effect of the first ten orders is 14.84%. The natural vibration frequency of the bridge decreases gradually with the increase of water depth. The maximum effect of the first five orders is 3.33%.

Stiffness-based structural health monitoring methods are widely used for detecting the damage in a structure. These stiffness-based structural health monitoring methods uses change in natural frequencies and modeshapes for damage detection. These methods are based on identifying the change in stiffness of the healthy and damage structure to predict the damage in the structure. These stiffness-based methods are not efficient for detecting a small damage in a structure as there is a negligible change in natural frequencies and modeshapes due to a small damage in a structure, however the damping characteristics of the structure are highly sensitive to the damage in a structure. In this paper, new damping-based damage detection procedure has been proposed. In the proposed procedure, the changes in damping matrix of the structure has been used to detect the damage in the structure. The proposed procedure is able (or can) to detect both the location of the damage and the extend of the damage in the structure. The proposed procedure of damping-based damage detection is a 2-step procedure. In the first step, damping matrices of both the healthy and damage structure are identified and in the second step, the identified damping matrices are used for damage detection. Numerical and experimental case studies are presented to demonstrate the effectiveness of the proposed procedure. The results have shown that the proposed damping-based damage detection procedure can be used for detecting damage in a structure with confidence.

A thermal protection system (TPS) is designed and fabricated to protect a hypersonic vehicle from extreme conditions. Good condition of the TPS panels is necessary for the next flight mission. A loose bolted joint is a crucial defect in a metallic TPS panel. This study introduces an experimental method to investigate the dynamic characteristics and state of health of a metallic TPS panel through an operational modal analysis (OMA). Experimental investigations were implemented under free-free supports to account for a healthy state, the insulation effect, and fastener failures. The dynamic deformations resulted from an impulse force were measured using a non-contact three-dimensional point tracking (3DPT) method. Using changes in natural frequencies, the damping ratio, and operational deflection shapes (ODSs) due to the TPS failure, we were able to detect loose bolted joints. Moreover, we also developed an in-house program based on a modal assurance criterion (MAC) to detect the state of damage of test structures. In a damage state, such as a loose bolted joint, the stiffness of the TPS panel was reduced, which resulted in changes in the natural frequency and the damping ratio. The calculated MAC values were less than one, which pointed out possible damage in the test TPS panels. Our results also demonstrated that a combination of the 3DPT-based OMA method and the MAC achieved good robustness and sufficient accuracy in damage identification for complex aerospace structures such as TPS structures.