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Accurate frequency estimation is crucial for researchers and engineers engaged in audio processing, communication, and vibration analysis. In the case of short signals containing low-frequency components and a non-integer number of periods, conventional frequency estimation algorithms, such as DFT, prove inadequate in precisely identifying signal frequencies due to inherent limitations in frequency resolution and the presence of the leakage phenomenon. Interpolation methods offer the potential to enhance frequency estimation by discerning frequencies at intermediate positions within the spectrum. Precisely determining amplitude values across spectral bins is critical when employing such methods. Remarkably, while the initial phase of a signal can significantly alter the spectrum, its influence on amplitude distribution remains an aspect yet to be thoroughly researched. In this study, we use Python to implement the DFT algorithm and analyze how the initial phase affects the results. We are conducting tests using generated sinusoidal signals and signals processed with Hamming and Hanning windowing functions to determine the extent of changes in amplitude. The findings indicate that a signal's time shift can influence the spectrum significantly, resulting in inaccurate frequency estimations and erroneous conclusions in signal analysis. [ABSTRACT FROM AUTHOR]

The current paper explores a novel approach for determining temperature variations by integrating the modal parameters and AI techniques. The research focuses on the development of a comprehensive dataset for training an AI model encompassing an analytical method that considers thermal conditions and natural frequencies. Traditional methods of temperature measurement, like infrared and platinum resistance thermometers, often face limitations in terms of accuracy, especially in complex or dynamic environments having an uncertainty of ±3.6 °C [1], respectively ±0.2 °C [2]. In this study, we propose a methodology that harnesses the inherent relationship between axial loads caused by temperature variations and the change in natural frequencies of a double clamped steel beam. The measured natural frequency data is collected and fed into the AI model, specifically, for a robust temperature estimation, obtaining a maximum predicted temperature deviation of 0.386 °C. [ABSTRACT FROM AUTHOR]

This paper introduces a device dedicated to acoustic excitation for modal analysis of plates. A particular setup is requested since the system should produce acoustic excitation with high power in the 10...120 Hz frequency range. The system comprises a signal generator, an amplifier powered by a car starter or a battery, and a subwoofer. This system permits setting the generated frequency around the resonance frequency with reasonable frequency and amplitude stability. We present the system's design and test its performance on a rectangular plate. In our laboratory experiments, we achieved the desired structural behavior. [ABSTRACT FROM AUTHOR]

Low-Level Virtual Machine (LLVM) compiler infrastructure is a useful tool for building just-in-time (JIT) compilers, besides its reliable front end represented by a clang compiler and its elaborated middle end containing different optimizations that improve the runtime performance. This paper specifically addresses the part of building a JIT compiler using an LLVM with the scope of obtaining the hardware architecture details of the underlying machine such as the number of cores and the number of logical cores per processing unit and providing them to the NUMA-BTLP static thread classification algorithm and to the NUMA-BTDM static thread mapping algorithm. Afterwards, the hardware-aware algorithms are run using the JIT compiler within an optimization pass. The JIT compiler in this paper is designed to run on a parallel C/C++ application (which creates threads using Pthreads), before the first time the application is executed on a machine. To achieve this, the JIT compiler takes the native code of the application, obtains the corresponding LLVM IR (Intermediate Representation) for the native code and executes the hardware-aware thread classification and the thread mapping algorithms on the IR. The NUMA-Balanced Task and Loop Parallelism (NUMA-BTLP) and NUMA-Balanced Thread and Data Mapping (NUMA-BTDM) are expected to optimize the energy consumption by up to 15% on the NUMA systems. [ABSTRACT FROM AUTHOR]

Signals of short duration and containing a small number of cycles require special procedures if the precise estimation of their frequencies is intended. In this paper, we present an algorithm that allows accurate estimation of frequencies and simultaneously explains the decision regarding the prediction made. We first show why predictions regarding the frequency of signals mentioned above can contain significant errors and the prediction dependency on the analysis time. We then prove that the errors are systematic, and it is possible to train a neural network to quantify the errors and later correct the predictions. The algorithm also indicates the level of error by analyzing the signal-to-noise ratio. The algorithm was tested for numerous similar cases and proved to be reliable. At the end of the paper, we present how to use the algorithm using a signal generated with a known frequency. [ABSTRACT FROM AUTHOR]

When considering damage detection using the natural frequencies of structures, small frequency drops can indicate either the presence of cracks or a temperature change. This change can lead to additional stress affecting the modal parameters for specific structures, making it much harder to detect, locate, and evaluate damage accurately. The current research aims to describe a method for detecting transverse cracks in beams, considering temperature variations. The considered beam is fixed at both ends, thus inducing axial forces when the temperature is increased. The influence of temperature is considered using adjustment coefficients developed for each vibration mode. This coefficient can be used to accurately calculate the natural frequency for an intact or damaged beam. An analytical method for determining the natural frequencies caused by the changing temperature and the presence of a transverse crack is described and used to generate data for training a feedforward artificial neural network (ANN). The ANN's capability of determining the position of transverse cracks in double-clamped beams subjected to small temperature changes is proven by creating numerical simulations with known crack positions and thermal conditions for testing the developed method. [ABSTRACT FROM AUTHOR]

The paper focus on showing using statistical analysis the relevance of vibration, temperature, and humidity on a crimped connection between a copper wire and copper terminal. As a primary metric it was used, as baseline, the behavior of the resistivity of a crimped assembly after vibration, humidity, and temperature tests in order to analyze and conclude if there is a significant relation between all these environmental factors and the crimped height. The core activity of this experiment consists in the analysis performed on 50 crimped assemblies where the main dimensional characteristics were achieved using a specific crimping normative, followed by a sequence of environmental testing steps, in order to obtain a significant number of data points that enable us to create a proper statistical model to analyze and conclude the influence of vibration (one of the main environmental factors tracked) over the crimped assembly. [ABSTRACT FROM AUTHOR]

Ultrasonic welding parameters originally provided by the components supplier caused negative pull/peel tension results. In this paper, we present a method to find the optimal parameters for the ultrasonic welding of copper elements. These elements represent components inside an electrical harness from automotive industry: coper plate and copper wire strands. The design of experiments (DoE) was used as a method within the Six Sigma approach. We succeeded in obtaining welding parameters that ensure successfully passing the pull/peel tension test. [ABSTRACT FROM AUTHOR]

This paper presents a method for detecting a crack in simply supported beams by identifying its location and severity (depth). The method is based on the measured natural frequencies for several bending vibration modes of an intact and cracked beam and the Particle Swarm Optimization (PSO). To explain the approach, we calculate the relative frequency shifts (RFS) for eight vibration modes for all possible damage cases. To this aim, we use a mathematical relation deduced in previous research. Next, we monitor the natural frequencies, and in case of arising changes, we calculate the RFSs. We subtract, separately for all modes, the measured RFSs from all calculated RFSs. Considering the absolute values the subtractions achieve, we obtain eight surfaces that achieve elevation zero if the calculated and measured RFSs coincide. The zero-elevation points form curves with different shapes for the different vibration modes. The intersection of these curves, thus the location where all surfaces have zero elevation, indicates the damage location and severity. Adding the elevation values of the eight surfaces point by point, we obtain a new surface that has two points (due to symmetry) with zero elevation. The coordinates of these points indicate the damage parameters. We use the generated surface as an objective function and find the coordinates of the minima involving PSO. Using this method, we accurately identified the damage location and severity. [ABSTRACT FROM AUTHOR]

Structural health monitoring plays a crucial role in ensuring the integrity and safety of engineering structures such as steel beams. This research paper presents a comprehensive methodology for detecting transverse cracks in beams with a constant section and any boundary conditions. The proposed approach utilizes the normalized squared modal curvature of the beam, the damage severity, and the natural frequency of the undamaged beam. By analyzing the natural frequencies of both the undamaged and damaged states, Relative Frequency Shift (RFS) values are obtained. Subsequently, the Damage Location Coefficients (DLC) are calculated by normalizing the RFS values. These DLC values are then employed to establish a comprehensive database of known damage signatures, enabling the training of an artificial neural network (ANN) in MATLAB. The trained ANN can predict the locations of damages for new scenarios by utilizing DLC values obtained from measurements. To validate the effectiveness of the ANN, extensive simulations using Finite Element Method (FEM) and experimental measurements are conducted on a steel cantilever beam. The results demonstrate the ANN's capability to accurately predict the locations of transverse cracks, showcasing its potential as a reliable tool for structural health monitoring of steel beams. [ABSTRACT FROM AUTHOR]

Artificial intelligence is often used to assess the integrity of engineering structures. Many methods are available to assess different types of damage, but the correctness of the results is not proven until local inspection methods are applied. Therefore, there is a need to develop a tool that can estimate the accuracy of the assessment process through a supplementary intervention. In this paper, we propose and test a procedure to establish the accuracy of the damage assessment results, which is the follow-up of a normal damage assessment process. First, we assess the damage involving a method previously developed by the authors that consider the relative frequency shifts (RFS) for several bending vibration modes. The method has the support of artificial neural networks (ANN). Applying this method, we estimate the location and severity of the damage. Next, we apply a procedure that presumes first to calculate the modal curvatures and the resulting damage location coefficients (DLC) for this location. Then, we normalize the RFSs used in the assessment process and compare them with the DLCs derived analytically for the presumed damage location. Finally, we compare the DLCs with the normalized RFSs via the Euclidian distance. This comparison shows how accurately we assessed the damage location, the smaller the distance, the better the prediction. Applying this procedure as a follow-up of a standard damage detection process, we know the accuracy of the assessment prediction realized with a standard detection method. If the accuracy is unsatisfactory, we can use an ANN model that is trained with data from the supposedly defective area. [ABSTRACT FROM AUTHOR]

The paper presents the strain energy of the circular plate clamped all around through a relation obtained analytically and the graphic representation of the modal shapes and the maximum normalized strain energy along the x axis. Depending on the number of nodal circles s and the nodal diameters n, the maximum strain energy can be both in the center of the circular plate clamped all around, as well as the first ventral points from the center of the circular plate towards the outside of the plate. [ABSTRACT FROM AUTHOR]

The first part of the paper presents a study regarding the dynamics behavior of thin circular plate clamped all around. An analytical investigation is performed and the results in terms of mode shapes are used to highlight the plate's dynamics. The modal shapes are obtained using Bessel functions and their graphic representation is presented in 3D by using MS Excel software. [ABSTRACT FROM AUTHOR]

In the second part of the paper, the dynamic behavior of a doubly clamped beam is presented, where the right clamped end of the beam is weakened by introducing a weakening coefficient. The analytical calculation is based on the determination of the bending moment from the weakened clamped end expressed as a function of slope, after which the modal function, strain energy, and the characteristic equation are determined to obtain the eigenvalues of the first six vibration modes depending on the weakened coefficient of the clamped end. The obtained mode shapes and strain energies are determined for seven values of the weakened coefficient. [ABSTRACT FROM AUTHOR]

Using analytical equations, the paper aims to solve the dynamic behavior of beams where a clamped end of the beam does not respect the ideal boundary conditions by introducing a weakening coefficient. In the paper, the characteristic equation for determining the eigenvalues and the relationship of the modal function and strain energy are derived. The results show the first six vibration modes for different values of the weakening coefficient which is considered in the clamped end and the evolution of the strain energy. [ABSTRACT FROM AUTHOR]

For maintaining the safe operation of structures, it is necessary to develop SHM methods that can detect not only the presence of cracks in the structure but also any alterations of its fastening conditions. The current paper presents a method for developing an Artificial Intelligent model that can detect if a beam is affected by transverse cracks and at the same time, by improper boundary conditions. To this aim, a cantilever steel beam is considered as the in the current study. The training data for the artificial neural network (ANN) is created using an original analytic method which allows calculating the natural frequency loss caused by the occurrence of transverse cracks even if the beam is improperly fastened. The intelligent model is trained by employing the MATLAB software and tested using data acquired from numerical simulations. The results show very high accuracy in determining the presence of transverse cracks, and the capability of detecting the presence and severity of improper clamping conditions. [ABSTRACT FROM AUTHOR]

During functioning time, structures such as beams are subjected to a variety of loads caused by the working conditions and environment, which can lead to the development of cracks. The current research is concerned with detecting the presence and location of two transverse breathing cracks, in cantilever beams. Starting from the known fact that damages produce a stiffness degradation in structures altering their dynamic parameters, we performed modal simulations of damaged beams to determine their natural frequencies. By using the simulation data, we trained an artificial neural network (ANN), using the feedforward backpropagation algorithm, that is capable to detect the presence of the cracks, their position and for the case when the damages are in proximity, the model can determine if the cracks occur on the same face or opposite faces. [ABSTRACT FROM AUTHOR]

Evaluating the integrity of structures is an important issue in engineering applications. The use of vibration-based techniques has become a common approach to assessing cracks, which are the most frequently occurring damage in structures. When involving an inverse method, it is necessary to know the influence of the position and the geometry of the crack on the modal parameter changes. The geometry of the crack, both in size and shape, defines the damage severity (DS). In this study, we present a method (DS-SHC) used for estimating the DS for closed and open transverse cracks in beam-like structures using the intact and damaged beam deflections under its weight and a Stochastic Hill Climbing (SHC) algorithm. After describing the procedure of applying DS-SHC, we calculate for a prismatic cantilever beam the severities for different crack types and depths. The results are tested by comparing the DS obtained with DS-SHC with those acquired from dynamic tests made using professional simulation software. We obtained a good fit between the severities determined in these two ways. Subsequently, we performed laboratory experiments and found that the severities obtained with the DS-SHC method can accurately predict the frequency changes due to the crack. Hence, these severities are a valuable tool for damage detection. [ABSTRACT FROM AUTHOR]

In this paper a new analytical solution for solving the issues that arise in determining the correct form of the eigenmodes, for the case of simply supported on two opposite edges and clamped on the other two of a rectangular plate, is described. The case of a homogenous plate, isotropic, with constant thickness and uniformly distributed weight, and dynamically driven in the direction normal to the plane of the plate with a median surface in the xOy plane is considered. The deformed shape of the middle area Z(x, y) is analyzed. The theory of elasticity states that this phenomenon can be described by a bi-harmonic differential equation of smooth plates having constant thickness. However, the eigenfunctions obtained for this scenario, lead to eigenmodes representations which are accurate only for modes n=1 and m=1. In this paper it is shown that the proposed analytical solution accurately describes the eigenmodes for the above mentioned plate, with the given limit constraints, for every m and n modes. Moreover, this new solution stands out for its simplicity. MatLab environment was used for simulations. The results obtained using the proposed solution were compared with the results obtained by means of classical method. From the analysis we carried out, we observed a symmetrical distribution of the eigenmodes, on both sides of the equilibrium position. [ABSTRACT FROM AUTHOR]

Real beams have non-ideal boundary conditions and it is necessary to use new models to determine the real modal parameters. Models that use ideal conditions do not fully reflect reality and can lead to unsatisfactory description of the dynamic behavior. The hinged – hinged boundary conditions, which is in the focus of the paper, are not analyzed as a single beam, but as a continuous beam with three spans, free at the ends. The continuous beam with three spans is analyzed for cases in which the intermediate supports can occupy any position along the length of the beam, by an analytical solution of the problem, with the example of cases when the intermediate supports are located very close at the free ends of the continuous beam, thus simulating the real case for an hinged beam at both ends; the situation in which the intermediate supports are very close to one of the ends of the beam, thus simulating the real case of the clamped beam, with an imperfect clamped end; and the situation in which the intermediate supports are very close located anywhere on the beam length, thus simulating the hypothetic case with a continuous beam free at the ends and fix on the hinged supports. The analytic results are compared with numerical results by using finite elements method [ABSTRACT FROM AUTHOR]

Because our infrastructure is aging and approaching the end of its intended functioning time, the detection of damage or loosening of joints is a topic of high importance in structural health monitoring. The most desired way to assess the health of engineering structures during operation is to use non-destructive vibration-based methods that can offer a global evaluation of the structure’s integrity. A comparison of using different modal data for training feedforward backpropagation neural networks for detecting transverse damages in beam-like structures that can also be affected by imperfect boundary conditions is presented in the current paper. The different RFS, RFSmin, and DLC training datasets are generated by applying an analytical method, previously developed by our research team, that uses a known relation, based on the modal curvature, severity estimation of the transverse crack, and the estimated severity for the weak clamping. The obtained dataset values are employed for training three feedforward backpropagation neural networks that will be used to locate transverse cracks in cantilever beams and detect if the structure is affected by weak clamping. The output from the three ANN models is compared by plotting the calculated error for each case. [ABSTRACT FROM AUTHOR]

Over functioning time, structures can be affected by multiple types of damages caused by fatigue, improper production methods, or exceeding loads. The current paper describes a method for evaluating the severity of transverse cracks that are present in beam-like structures based on changes in the natural frequencies. Because the presence of damage has a negative impact on the energy that a beam can store in the affected section, it is possible to find the influence of the crack on any other position along the beam, considering the stored normalized energy in that location. The technique is based on a mathematical relationship that provides the exact solution to the frequency changes of the bending vibration modes, considering two terms. The first term is related to the tensile energy stored in the beam, and the second term considers the increase of flexibility due to cracks, for this reason, damage assessment is performed in two stages; first, the location of the crack is found and then an assessment of its severity is performed. In this study, the aim is to test the developed method for estimating the severity of transverse cracks for different sections and lengths of beams [ABSTRACT FROM AUTHOR]

In the case of damage detection, it is important to estimate the frequencies accurately. DFTbased methods provide us with amplitude-frequency pairs, but displayed frequencies carry important errors in the case of short signals. On the other hand, the amplitudes displayed for a sinusoidal signal with different time lengths describe approximately a sinc function. When involving interpolation to find the maxima of the sinc function, to which the real amplitude of the signal corresponds, it is necessary to ensure the existence of at least three points on the main lobe of the sinc function. To this aim, we apply zero-padding to the original signal in such a way that its length is doubled. The frequency estimation method proposed in this paper involves an artificial neural network (ANN). The three amplitudes taken from the main lobe determined for all considered signal lengths are the input values used to train the network. The correction term that allows us to evaluate the frequency will be the target. Following the simulations made, it is found that using normalized data sets we can estimate any frequencies, irrespective of the frequency with which the network was trained. It applies to any signal length, and any signal amplitude. [ABSTRACT FROM AUTHOR]

The more our infrastructure is aging, the risk of structural failure is higher, making the detection of damage using modal parameters a very important factor that can be applied in structural health monitoring. The most desired way to assess the health of engineering structures during operation is to use non-destructive vibration-based methods. In the current paper, a modal approach using a machine learning technique by training a feedforward backpropagation neural network for detecting transverse damages in simple supported beamlike structures is presented. A method for analytical determination of the training data is used and the obtained dataset values are employed for training an ANN that will be used to locate and evaluate the severity of transverse cracks in cantilever beams. The output from the ANN model is compared by plotting the calculated error for each case in comparison with FEM results using the SolidWorks simulation software. [ABSTRACT FROM AUTHOR]

As the infrastructure ages and nears the end of its estimated operating time, the detection of damages becomes a major issue in structural health monitoring (SHM). In this paper, the authors propose an analytical approach for generating the data needed to train a Random Forest model (RF) that will perform the SHM task, namely, to detect, locate, and assess the severity of transverse cracks in beam-like structures. Using an original method, we calculate the relative frequency shifts (RFS) for different damage scenarios and use the generated data to train the RF model. Subsequently, the validation of the RF model is performed using data obtained from FEM simulations using different mesh sizes, for different damage scenarios on steel beams. The results indicate that the RF model can detect the presence of the defect and find the position and depth of the transverse cracks very precisely if the crack is located in the area where the beam achieves the maximum bending moment. [ABSTRACT FROM AUTHOR]

In this paper, we propose a model for detecting transverse cracks in simply supported beams, which can be part of more complex structural systems. The relative frequency shifts of the structure are considered a basis for damage identification. An original method developed by the authors is employed to evaluate the required modal parameters. A multi-stage optimization approach based on the rigidity loss suffered by the affected structure is employed to accurately recognize the locations of potential cracks. The outcome presented in this research shows the computational ability of the proposed model to indicate the presence and location of damages in beam-like structures. [ABSTRACT FROM AUTHOR]

We propose a continuous model for rectangular plates that involves a mesh of slender interconnected beams. These beams are disposed orthogonally. The advantage of this model is that simple equations are involved and the behavior of the plate is accurately described. After a brief description of the model, we present an application written in the Python programing language that allows calculating the mode shapes for rectangular plates with various boundary conditions. The mode shapes achieved with the application for a specific plate are found to be similar with those obtained from simulation involving the SolidWorks software. In consequence, we conclude that the proposed model is reliable and the application developed on this base can be used to study the behavior of rectangular plates with different boundary conditions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Frequency estimation for short-time signals is difficult because the raw frequency resolution obtained. The frequency for these signals fall usually at an inter-line position, and is far from the frequency displayed at the spectral line. To get a better frequency estimate, interpolation methods are used to find the peak between the two spectral lines on which the biggest amplitudes are obtained. The number of points involved in the interpolation are two or three. The inter-line position at which this maximum is found is considered to correspond to the true frequency. This paper presents a comparison of the most common interpolation methods that can be used to increase the precision of the frequency estimation, so necessary in the processes of structural health and condition monitoring. An analysis of the accuracy obtained by these methods is made for a generated signal with an acquisition time of around 1 second. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper proposes an analytic relation for the deflection of a cantilever beam with a transverse crack subjected to dead load. The mathematical relation is deduced involving the decreased capacity of the beam to store energy, which is in direct relation with the crack position and depth. Eventually, the validity of the relation is proved by means of the finite element method. [ABSTRACT FROM AUTHOR]

In this paper we propose a procedure to correct Jain's algorithm, which in certain situations fails in correctly estimating the frequency by indicating frequency values that are very far from the real frequency. It happens because the two points considered for the method proposed by Jain are not on the same lobe. Thus, a method is proposed according to which these points are chosen so that the results are improved. [ABSTRACT FROM AUTHOR]

We introduce in this paper an application developed in the Python programming language that can be used to generate digital signals with known frequencies and amplitudes. These digital signals, since have known parameters, can be used to create benchmarks for test and numerical simulation. [ABSTRACT FROM AUTHOR]

Detection of damage requires an accurate estimation of the natural frequencies of the monitored structure. This paper introduces an algorithm implemented in Python which improves the frequency readability by increasing the number of spectral lines without requiring a signal extension in the time domain. We achieve this by overlapping several spectra calculated from the acquired signal repeatedly shortened. In this way, the overlapped spectrum gets an increased number of spectral lines. The dense mesh of spectral lines permits us to obtain a fine frequency resolution without being necessary an extension of the signal in the time domain. The high density of the spectral lines ensures a sufficient number of points on the main lobes that permits performing an efficient quadratic polynomial interpolation to find the maximizer. It represents the amplitude of the real frequency and is typically located on an inter-line position, thus cannot be found by standard frequency estimation. We implemented the algorithm in Python and tested it successfully for generated signals, containing one or more harmonics, with known frequencies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper presents research done by means of numerical simulation on a rigid structure isolated with friction pendulums. To this aim, we design friction pendulums which differ by the shape and dimension of the cylindrical sliding surface, respectively by the friction coefficients. Our target was to find out how the structure responds to a given excitation when the structure is equipped with diverse friction pendulums. A sinusoidal excitation with the frequency of 1 Hz is applied and the response in terms of displacements is captured. We found that the frequency of the structure does not change with the FP radius but the amplitude of the displacement is strongly dependent on this parameter. Because the circular and elliptical sections of the FP provide the structure with different natural frequencies, the resonance is achieved at other radii. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper examines how a transverse crack near the fixed end of a beam affects the natural frequency drop. It is known that the decrease in the frequency due to a crack depends on the position of the damage and its severity. This happens because the slice of the beam on which the crack is located changes its stiffness. Consequently, the damaged beam is no longer able to store the identical amount of energy as the healthy one. In addition, the field of stresses and deformations on an extended area around the crack is disturbed. This alteration can manifest freely for most positions of the crack along the beam. For this case, there is a direct relationship between the defect position and the frequency change, given by the modal curvature of the beam. Close to the fixed end, the field of stress and deformation is hindered on one side of the crack by the fixed end condition. In this way, the crack will produce a lower frequency drop compared with what it is expected. We performed simulations to obtain the frequency drop if the crack is located very close to the fixed end. With these values, we plot the regression curve and estimate the frequencies which should result for a crack located exactly on the fixed end of the beam if symmetric fields of stress and strain are possible. The results are necessary because the frequency drop characterizes the damage severity, further used in the damage detection processes. [ABSTRACT FROM AUTHOR]

The objective of the paper is to calculate the velocities and accelerations for some points of the punching cards mechanism and to compare the results calculated through grapho-analytical method with the SolidWorks Motion results. [ABSTRACT FROM AUTHOR]

Accurate frequency assessment is nowadays required in the mechanical engineering applications. Because in the standard methods that allow finding the real frequency occur errors, which come from the fact that they depend largely on the acquisition time, we set out to improve these methods. The purpose of this work is to find the maximum amplitude of the interpolation curve that passes through two amplitude peaks on two adjacent spectral lines. The method presented in the paper ensures a high precision when determining the frequency indicated by the maximizer. [ABSTRACT FROM AUTHOR]

The retrieval and storage of information from historical earthquake records are very important for the study of seismic activity and the prevention of the danger that earthquakes represent in areas with intense seismic activity. This is possible due to modern techniques and methods of processing, converting old data into digital data and storing them on online databases. This paper presents some important web-based database that provides tools for searching, selecting and downloading ground motion data. [ABSTRACT FROM AUTHOR]

Estimating the harmonic components of a signal is based on calculating the signal energy on certain spectral bins that position is defined by the signal time length. Because of this mode of calculation, a difference between the true frequency and the estimate is usually found. In this paper, we present an advanced frequency estimation method, which searches first for the time length for which an entire number of cycles is contained in the signal and afterward calculates the Discrete Fourier Transform (DFT). The results have been found significantly closer to the true frequency as those obtained by a standard DFT applied to the original signal, but it still depends on the number of cycles involved. To further improve the estimation results we propose a methodology to make a correction depending on the number of cycles and sampling frequency. [ABSTRACT FROM AUTHOR]

Since the beginning of the last century, worldwide, researchers and visionaries have spent a lot of time and energy to develop devices capable to use the centrifugal forces for generating linear motion. The present paper presents an inertial driving system designed to produce a propulsion force from the kinetic energy of 8 steel balls which are rotating on an eccentric circular path. The balls are placed between two rotating discs provided with radial slots. After presenting the equations of motion for the steel balls and deducting the propulsion force of the driving system, the paper pays a particular attention to the investigations on the influence of the geometry of the device on the generated linear force. Based on the obtained findings, the authors are confident about the system's ability to produce propulsive force and linear motion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper presents a study regarding the effect of the friction coefficient on the behavior of structures isolated by friction pendulums. A laboratory-scale structure and its model created in SolidWorks are employed in the research. The excitation, ensured by a shaking table, follows a displacement after sinusoidal and complex rules. The study revealed the frequency at which the chosen friction pendulum assures efficient isolation is higher then 3 Hz irrespective to the friction coefficient. Experimental results coincide with those obtained from simulations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]