تعیین شدت و محل ترک در تیر اویلر-برنولی، با استفاده از سیگنال حوزه زمانی پاسخ ارتعاش آزاد و بهینه سازی به روش ازدحام ذرات، تحت بار ضربه

در این مقاله روشی جهت تشخیص خرابی تیر اویلربرنولی مبتنی بر ابر المان، ارائه شده است. روش ارائه شده با استفاده از سیگنال حوزه زمانی پاسخ ارتعاش آزاد، موقعیت و عمق ترک در تیر اولر - برنولیِ مدل شده با سختی اصلاح شده بر اساس مدل فنر پیچشی را، با سرعت و دقت بالا ارائه می دهد. پاسخ های تاریخچه زمانی همان شتاب در لبه المان های الاستیک تیر است که در این پژوهش در معرض بار ضربه، اندازه گیری شده اند. شتاب های این سازه از روش انتگرال گیری زمانی نیومارکبتا محاسبه می گردد. در ابتدا تابع هدف مسئله تشخیص خرابی، جهت بهینه سازی به روش الگوریتم ازدحام ذرات، تعریف شده و با حل مسئله بهینه سازی در محیط متلب، شدت و محل ترک های عرضی محاسبه می شود. به منظور ارزیابی دقت روش ارائه شده، 3 نمونه تیر در نظر گرفته شده است. نتایج حاکی از آن است که پس از حداکثر 50 بار اجرای الگوریتم، خطای محاسباتی کمتر از 10 درصد در داده های محل و عمق ترک وجود خواهد داشت.

Determining the severity and location of cracks in the Euler-Bernoulli beam, using the time domain signal of free vibration response and particle optimization method, under impact load

In this paper, a crack detection method is presented to detect EulerBernoulli beams containing arbitrary number of transverse cracks. The proposed method uses the time domain signal of the free vibration response to provide the position and depth of cracking of the EulerBernoulli beam that is modeled with a modified stiffness using the Spring model, with high accuracy and precision. The time history responses used in this paper are nodal computational accelerations at certain points of the beam exposed to impact load. The acceleration of the nodes is calculated with the Newmark beta method at the edge of the elastic beam`s superelements. Initially, using the computational time history of the damaged beam and the analytical model of the EulerBernoulli beam, the objective function of the failure detection problem, to be optimized by particle swarm algorithm, is defined and, intensity and location of transverse cracks are calculated by solving the optimization problem in Matlab environment. In order to determine the accuracy of the proposed method, three beam samples with different cracks and loadings are considered. In the first sample, the crack supposed to be in the superelements of beam and the beam considered to be with four elements as superelements. The second one has ten elements and same loading as previous. The third one has twenty elements and the loading is on the second element. All of the loadings are impulse loads. The comparison of the results of a four elements beam with the primitive conditions shows that accuracy of the deducted results were exactly matched. For the ten element beam, the results were satisfying but in the twenty element beam with asymmetric loading, obtained results indicate imprecise match.To determine the accuracy of the developed model in real environmental conditions, different percentages of noise were added to the data of all three samples. These noise addition to data, contain 1, 3, 5 Percentages of noise. The results show that the model presented in the presence of noise also provides accurate results and the model is not sensitive to the presence of noise in the data applied to three samples. Considering different number of elements in each sample, no convergence was observed, Also the results were not sensitive to the location of impact load applied on the samples.The results of this study indicated that asymmetric cracking and loading variation are very effective in predicting beam failure. The results also indicate that variable reduction is very effective on the accuracy of results.Having more cracks and therefore more elements to analyze will yield to less accurate results. To lessen these inaccuracies, it can be practical to achieve better results by assuming the location of crack is constant in the element length if the depth of crack be the matter of importance.The number of iterations that have been executed, indicate that the pace of convergences in the developed process is less than when PSO deployed solely. This speed rate for obtaining results makes the developed method practical for solving crack detection problems in structures.