Papers by Cristian Tufisi
The current paper presents an algorithm for locating transverse cracks present in Euler-Bernoulli... more The current paper presents an algorithm for locating transverse cracks present in Euler-Bernoulli steel beams, by considering the relative frequency shifts (RFSs) measured for the weak-axis vibration modes and the mode shape curvatures. To apply the algorithm, we first determine, by means of the finite element method (FEM), the natural frequencies for the first four bending vibration modes for the healthy beam fixed-free and fixed-fixed end conditions. Afterward, we introduced transverse cracks with known depth and location and determined again the natural frequencies. As a next step, we use an original algorithm to plot the potential severity curves (PSCs) for the four modes and find the intersection, which indicates the crack severity and location. It was found that the method is reliable for determining the location of transverse cracks just by using the measured natural frequency and the squared normalized modal curvatures (SNMCs) for both imposed boundary conditions.
Detection of Multiple Cracks Using an Energy Method Applied to the Concept of Equivalent Healthy Beam
Lecture Notes in Mechanical Engineering, 2019
We introduce herein the concept of global stiffness of a damaged beam, and the Equivalent Healthy... more We introduce herein the concept of global stiffness of a damaged beam, and the Equivalent Healthy Beam (EHB) as a damage model. This model simplifies the process of assessing multiple cracks in beams. It consists of a thinner beam with constant cross-section, but with unchanged mass, which stores in each vibration mode identical energy as the damaged beam. Hence, the model has similar frequencies as for the damaged beam. We estimate the amount of the stored energy from the beam deflection under dead mass. Each additional crack provokes a deflection increase, and consequently the beam stores less energy. The resulted EHB becomes therefore thinner. We performed simulations for beams with transversal cracks which are present on the opposite beam faces. By iteratively removing one crack relative to the other, we obtained the values of the deflections and the eigenfrequencies for the first vibration modes. Comparing the separate frequency drop due to cracks with the effect of the concomi...
The paper presents the investigations made to evaluate a model that predicts the frequency shifts... more The paper presents the investigations made to evaluate a model that predicts the frequency shifts due to T-shaped cracks. We developed the model basing on the energy loss due to the decrease of the beam’s rigidity in the region of the crack which has a transversal and a longitudinal component, respectively. The algorithm includes a coefficient representing the energy fraction for the healthy and the damaged beam segment. These fractions are described involving the normalized square of the modal curvatures and get the form of an integral. To fast solve the integrals, we implemented the model in an application written in the Python programming language. This application solves numerically the integrals and a coefficient expressing the remained energy after damage results in form of a coefficient. We successfully tested the theoretical model against finite element simulation.
The paper presents a study regarding the vibration behavior of Euler-Bernoulli beams which have c... more The paper presents a study regarding the vibration behavior of Euler-Bernoulli beams which have cracks with complex shapes. The aim is to show that diverse orientations of the crack branches occurring in a given region of the structure produce different changes of the eigenfrequencies for the different vibration modes, dependent on the position and propagation angle of the crack. The research is conducted employing the finite element analyses, which are used to describe the dynamic response of a structure affected by a transversal open crack followed by two branches, each oriented at a different angle. These cracks are traditionally referred to as Y-shaped crack. We calculated the relative frequency shifts for the first six transverse vibration modes and extracted the damage signature for the considered branched crack location. The damage signatures can be used as patterns in damage detection procedures, transforming the procedure of detecting the crack position and severity from th...
Statistical Method for Damage Severity and Frequency Drop Estimation for a Cracked Beam using Static Test Data
We present in this paper a statistical method to estimate the severity of a transverse crack form... more We present in this paper a statistical method to estimate the severity of a transverse crack form the free-end deflections of a cantilever beam. To this aim, we carry out simulations involving the ANSYS software and register the free-end deflections resulted for different crack positions near the fastened end. By involving a statistical method, we find the damage severity which reflects the crack effect on the frequency drop if the crack is located exactly at the fixture. The accuracy of the achieved damage severity values is verified by comparing the calculated frequency drops for several crack locations with those obtained from simulations. We found that the damage severity contrived by involving the statistical method is accurate and can be successfully used to predict the dynamic behavior of a cracked beam.
The paper proposes modeling approaches of complex shape cracks. Structures may present many types... more The paper proposes modeling approaches of complex shape cracks. Structures may present many types of defects, of different irregular shapes and sizes, due to various reasons, and so it is very important for the model of the crack used to be accurate. There are three main categories for modeling of cracks; local stiffness reduction, discrete spring models, and complex models in two or three dimensions each proving to be reliable methods for generating finite element models.
A New Concept Regarding the Modeling of Steel Cantilever Beams with Branched Cracks: A Case Study
Identifying cracks in the incipient state is essential to prevent the failure of engineering stru... more Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we have found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the...
Exact solution for the severity of transverse cracks in prismatic beams
Journal of Physics: Conference Series, 2020
Identification of Delamination in Multilayered Composites
IOP Conference Series: Materials Science and Engineering
Automatic detection of L and T shaped cracks in semifinished casting products
IOP Conference Series: Materials Science and Engineering
This paper focuses on the accuracy of detecting the location of a complexly shaped damage present... more This paper focuses on the accuracy of detecting the location of a complexly shaped damage present in a cantilever beam. The study is carried out by involving the finite element method. At first, we have parametrically described the geometry of a branched crack and designed its discrete model. As a further step, we performed simulations to observe the changes in the static and dynamic behavior of the beam that occur in the presence of damage. Several types of Y-shaped cracks have been taken for these analyses. We have shown the beam has a diminished capacity to store energy and consequently the frequency decreases. The frequency shift phenomenon for the first mode of vibration was found to be in concordance with the changes in the deflection of beam’s free end. We derived on this basis a correction coefficient that considers the beam deflections in the intact and damaged state. This coefficient permits predicting the frequency shift due to a given crack. As the last step, we have suc...
A new predictive model to estimate the frequencies for beams with branched cracks
IOP Conference Series: Materials Science and Engineering
Detecting damage by using vibration signals is popular because it permits evaluating the structur... more Detecting damage by using vibration signals is popular because it permits evaluating the structural integrity without being necessary scanning of the whole structure. The effect of transverse cracks is presented in detail in the literature, but in reality, the cracks can shift the direction of propagation and even split, resulting in the so-called branched crack. The effect of this type of crack is less investigated due to its complexity. We herein propose a simple model to predict frequency changes that occur due to branched cracks. Initially, we present the effect of stiffness reduction along the damaged section on the structure's natural frequency. Next, we show that the predicted frequency drop is smaller that happens in reality. This is caused by the sudden cross-section reduction in the slice on which the transverse crack branch is. The phenomenon is similar to the stress concentration for static loads. We propose for dynamic systems a factor that considers the energy stored at the delamination ends. Considering this factor and the stiffness reduction on the damaged segment, we obtain accurate frequency changes due to any type of crack that extends in the longitudinal direction. The model is implemented in Python and tested successfully against simulation with dedicated software.
Studia Univesitatis Babes-Bolyai Engineering, 2020
This paper presents a method to find the severity of a crack for cantilever beams that can be use... more This paper presents a method to find the severity of a crack for cantilever beams that can be used to estimate the frequency drop due to the crack. The severity is found for the crack located at the location where the biggest curvature (or bending moment) is achieved. Because the fixing condition does not permit a symmetrical deformation around the crack, the apparent severity is smaller as the real one. The latter is found by the estimated value of the trend-line at the fixed end, it being constructed on points that consider the crack position (equidistant points in the proximity of the fixed end) and the resulted deflections.
This paper presents a method to find the severity of a crack for cantilever beams that can be use... more This paper presents a method to find the severity of a crack for cantilever beams that can be used to estimate the frequency drop due to the crack. The severity is found for the crack located at the location where the biggest curvature (or bending moment) is achieved. Because the fixing condition does not permit a symmetrical deformation around the crack, the apparent severity is smaller as the real one. The latter is found by the estimated value of the trend-line at the fixed end, it being constructed on points that consider the crack position (equidistant points in the proximity of the fixed end) and the resulted deflections.
Romanian Journal of Acoustics and Vibration, 2019
The paper presents the investigations made to evaluate a model that predicts the frequency shifts... more The paper presents the investigations made to evaluate a model that predicts the frequency shifts due to T-shaped cracks. We developed the model basing on the energy loss due to the decrease of the beam's rigidity in the region of the crack which has a transversal and a longitudinal component, respectively. The algorithm includes a coefficient representing the energy fraction for the healthy and the damaged beam segment. These fractions are described involving the normalized square of the modal curvatures and get the form of an integral. To fast solve the integrals, we implemented the model in an application written in the Python programming language. This application solves numerically the integrals and a coefficient expressing the remained energy after damage results in form of a coefficient. We successfully tested the theoretical model against finite element simulation
43rd International Conference on mechanics of Solids , 2019
In the current paper we aim to evaluate the accuracy of a previously developed method to determin... more In the current paper we aim to evaluate the accuracy of a previously developed method to determine the frequency drop of a cantilever beam having an L-shaped damage with a well-defined position and size. The method is based on the fact that the deformation energy lost by reducing a section of the beam is proportional to the deflection of the same beam under own mass. By setting the boundary and initial conditions for the cantilever, fixed at one end and free at the other, we applied equations of motion for the entire structure based on the Euler-Bernoulli beam model. By using the relation between the frequencies and the deformation energy we obtained a correction term that allows us to calculate the natural frequencies of the cantilever beam having a reduced section based on the frequencies of the undamaged beam. The method is applied through a program developed in the Python language by our research team. The obtained frequencies for the beam with a reduced section are compared with does deducted with the help of the ANSYS simulation software for the beam with an L-shaped crack. Tests performed to find the accuracy of the frequency estimates show that the results are very accurate and we concluded that this method can be used with confidence for modal analysis issues.
Analele Universitatii "Eftimie Murgu" Resita. Fascicula de Inginerie, 2018
The paper proposes modeling approaches of complex shape cracks. Structures may present many types... more The paper proposes modeling approaches of complex shape cracks. Structures may present many types of defects, of different irregular shapes and sizes, due to various reasons, and so it is very important for the model of the crack used to be accurate. There are three main categories for modeling of cracks; local stiffness reduction, discrete spring models, and complex models in two or three dimensions each proving to be reliable methods for generating finite element models.
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Papers by Cristian Tufisi