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We propose in this paper a method to detect cracks in circular plates clamped at the circumference. It consists in analyzing and interpreting the frequency changes that occur due to a circular arc crack. We show that the effect of the crack depends on the strain energy loss, which actually is proportional to the curvature achieved by the affected region in the radial direction. Three types of cracks are considered herein to demonstrate this dependency, differing by their length. Modal analysis is performed involving a professional simulation software for the intact plate, and that with the generated cracks. We found a perfect fit when we compared the curvature of the plate in the radial direction obtained with the analytical relation with the frequency values for the crack displaced along the radius. Therefore, using the curvature of several vibration modes we can obtain damage patterns that can be used to locate circular cracks.

In this paper we propose a protocol for economic decision-making by the management of an industrial enterprise, which wishes to set up a new production unit. The problem is finding the location of the new production unit, which will minimize the total transport cost, consisting of an amount of costs directly proportional to the distances between the new and existing locations. In order to obtain the optimum location, the QSB software package was used, which uses, besides the Manhattan model and the Euclidean and Euclidean quadratic distance measurement model

The paper presents a study dedicated to analyzing the sensitivity of structures with open contours to cracks. For this purpose, we analyze the particular case of the I-beam made by welding, for which we want to see how the frequencies of different modes of vibration change when a crack occurs in the weld joint between the web and the flange. The research is done using numerical simulations performed with the ANSYS program, from which the natural frequencies are obtained depending on the depth and extent of the crack. A large number of vibration modes and two types of boundary conditions are taken into account. We found that the frequency changes are small but still detectable and depend on the beam fixation mode. This makes it possible to detect cracks in the weld joint if the vibration modes where the decrease in frequency is significant are analyzed.

In this paper, we analyze the case of structural integrity assessment when the beams have several cracks. The relationship between the location and the severity of one crack and the resulting frequency shift is known. That is why we can design databases containing many defects for which we can calculate precisely the frequency changes and the subsequent damage location coefficients. When the natural frequency evolution of several vibration modes is monitored, we can find alteration due to the crack. Comparing the results of the measurements with the values contained in the database, for instance by involving a bin-by-bin dissimilarity estimator, we can find the location and severity of the crack. For multiple cracks, this approach was not investigated. In this study, we design a database for two cracks affecting at the same time the beam. For these cracks, which have various severities and locations, we calculated the frequency changes by applying the superposition principle. Afterward, we find the frequency shifts for a test structure by means of the finite element method. The comparison between the damage location coefficients in the database and the signature of the damages achieved by simulation is made by the software we have developed in Visual Basic for Application in Excel. We succeed to find the severity and the location of the two cracks for all considered crack configurations.

The paper presents a mathematical relation to express the effects of a T-shaped crack on beam-like structures. The study is performed by using the finite element method (FEM) and contrived analytical formulas for proving the existing correlation between deflection, strain energy, and natural frequency changes. The damaged beam static and dynamic behaviors are analyzed by means of the FEM. The frequency shift for the first mode of vibration derived directly was compared with the frequency alteration calculated involving the change in the beam deflection for several scenarios of the T-shaped crack. The frequency shift is derived using the relations between deflection and natural frequency. As the final step in the research, we compared the outcomes for the same crack with the results achieved from a beam suffering a loss of stiffness.

The paper presents a procedure to precisely estimate the natural frequencies of structures. It implies the acoustic excitation of the structure and the evaluation of the frequencies from the response signals, involving an advanced method developed by the authors. The study is performed on a cantilever beam. To demonstrate the efficiency of the contrived procedure, the values of the frequencies by applying this procedure are compared whit those obtained by standard frequency estimation made for the response to an impulsive excitation.

In this paper we started from a case study in which we wanted to develop an own methodology of designing lower rank productions systems, and of simulation-optimization of production flows, using several software’s. Because of it's complexity, the study is truncated, making it the subject of several specialized articles. In this article we calculate the efficiency of an assembly cell, using the software Flexible Line Balancing.

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.

We propose herein a mathematical relation to calculate the severity of transverse cracks which affect a prismatic beam. It is known that the damage severity depends on the depth of the crack located at the slice on which the biggest bending moment is achieved. The frequency drop due to this crack is proportional to the severity associated with it. For all other crack locations, the effect is diminished in relation to the curvature registered at the affected slice. It is essential to obtain a relationship to correctly express the severity with respect to the crack depth. To find it, we designed a model of a cantilever beam with cracks located near the fixed end. We observed that the deflection of the beam’s free end increases the closer the crack to the fixed end is, but after a certain limit, the deflection decreases. We concluded that the deflection decrease occurs because the deformation around the crack is restricted by the fixing condition. To find the true severity, we derived the pseudo-severity for six crack positions and estimate the severity using the linear and second-order polynomial regression curves. Next, we used twelve points for interpolation and found a very similar severity. Finally, we performed modal analysis for the beam with cracks at different positions and found the mathematical relation developed to predict frequency changes that involves the severity provides accurate results.

We propose in this paper a mathematical relationship to calculate the natural frequency shifts of beams due to multiple cracks. The relationship is based on the application of the superposition principle. A crack alters the frequencies for the bending vibration modes in a particular manner, with respect to the crack depth and location. We have shown that the affected beam have the same natural frequencies as a healthy beam with a smaller thickness; this thickness has to be calculated separately for each vibration mode. As a consequence, we can consider the next crack affects healthy beams, one different beam for each considered mode. Subsequent cracks affect a bigger number of beams. For the last crack, we have to calculate the frequencies for a number of beams that is the number of the considered vibration modes to the power equal with the number of cracks. To automate the process of calculating the resulted natural frequencies, we have written a program in Visual Basic for Excel Applications (VBEA), which permits finding the natural frequencies of a beam with up to nine cracks. This application can calculate the natural frequencies for four beam types: with fixed-free, fixed-fixed, simply supported and free-free restraints. The results obtained by calculating the frequencies for several damage scenarios and boundary conditions fit those obtained from simulations by involving the finite element method.

In this paper we start from the calculation of the product cost, applying the method of calculating the cost of hour- machine (THM), on each of the three cutting machines, namely: the cutting machine with plasma, the combined cutting machine (plasma and water jet) and the cutting machine with a water jet. Following the calculation of cost and taking into account the precision of manufacturing of each machine, as well as the quality of the processed surface, the optimal decisional version needs to be determined regarding the product manufacturing. To determine the optimal decisional version, we resort firstly to calculating the optimal version on each criterion, and then overall using multiattribute decision methods.

The paper includes a study on optimum batch calculation in designing the technology of execution of a welded structure within a company with mechanical profile, this being one of its main objects of activity. Because of the duration of different operations in the technological itinerary is not equal or in a multiple report, loading of machinery and workers cannot be done in a uniform manner, the production process being interrupted most often, narrow places and stocks large unfinished production, which is why we tried to determine an optimum manufacturing batch that would no longer allow these drawbacks. The solution of these problems is differentiated, considering the particularities of the manufactured product, the technological process, based on the economic analysis, aiming at the adoption of an optimal variant. The method provides the possibility to determine the influence of the size of the batch of parts on the duration of its production cycle.

This paper presents the determining of natural frequencies of plates without and with damages using the finite element method of SolidWorks program. The first thirty natural frequencies obtained for thin rectangular rectangular plates clamped on contour without and with central damages a for different dimensions. The relative variation of natural frequency was determined and the obtained results by the finite element method (FEM) respectively relative variation of natural frequency, were graphically represented according to their vibration natural modes. Finally, the obtained results were compared.

It is increasingly being applied by organizations to provide “soft” skills, not just technical training because technology can create realistic, interactive, computer-based simulations. The purpose of the paper is to present the way in which can be solved, using the WinQSB program, some types of problems. Sub modules as PERT/CPM and Facility Locations will be appealed, that is adequate solving the ordinance issues, respectively fabrications lines equilibration. Using this software in practice has a real contribution to the developed activities efficiency, insuring a high economy of time by eliminating routine activities tide to the classic way of solving the problem.

The paper presents some general considerations on the action of variable straines on the remanent tensions, strain cycles, stabilisation tests after welding operations and welded metallic constructions subjected to vibratio.

Based on experimental measurements, this paper presents the vibration analysis of a hydro generator that equips a Kaplan hydraulic turbine of a Hydropower plant in Romania. This analysis means vibrations measurement to different operating regimes of the hydro generator respectively before installing it and into operation, namely putting off load mode (unexcited and excited) respectively putting on load mode. By comparing, through the experimental results obtained before and after the operation of hydro aggregates are observed vibrations improvements.