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 in this paper a method to calculate the antiderivative of signals that have the integral close to null, as the signals measured on structures during earthquakes are. The method implies performing a series of numerical integration considering the initial value being zero. Afterward, the average value for the primitive function is calculated and considered as initial value: this solves the initial value problem with acceptable precision. Because of the minor errors, the second antiderivative that is the displacement in our case will gain a continuously slight increase. We overcome this problem by finding the trendline and extracting it from the signal representing the second antiderivative. In this way, we obtain accurate instantaneous values for the displacement as well. The algorithm, nominated as PySEMO, is implemented in the Python programming language and used to demonstrate the accuracy of the method. At the end of the paper, we make recommendations for the acquisition strategy to guarantee to find precise velocities and displacements. The algorithm can be used for other signals alternating around zero, e.g. those measured on rotating machines, as well.
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.
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.
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