تعیین میزان آسیب تیر دو دهانه به کمک روش رایلی

در این پژوهش به کمک روابط اساسی دینامیک سازه و مقاومت مصالح به دنبال درک بهتری از سازه‌های آسیب هستیم. در واقع، این مقاله روشی کاربردی ارائه می‌دهد که به کمک فرکانس طبیعی میزان شناخت از آسیب در تکیه‌گاه خود که می‌تواند ما را در بهسازی سازه کمک کند. در این روش تنها به دریافت فرکانس از سازه است و نیاز به کنترل سازه و حضور نیروی انسانی به‌صورت مداوم نیست. همان‌طور که نتایج نشان داد، پارامترهای دینامیکی نقش پررنگی دارند. آنچه حوزه پایش سلامت سازه‌ها و به‌خصوص ردیابی ترک را از یک‌ طرف بسیار جذاب و از طرفی خیلی سخت کرده عدم اطمینان قابل‌توجه آسیب در سازه است. در واقع از ایجاد آسیب در سازه تا تشخیص و ترمیم آن با عدم قطعیت بالایی روبه‌رو هستیم که کار را بسیار سخت و با هزینه محاسباتی بالایی مواجه می‌نماید. سازه مدل‌سازی و تحلیل شده در این مقاله با سه تکیه‌گاه آسیب‌دیده می‌تواند نسبت به مدل‌های ارائه شده قبلی که عموماً به‌صورت کنسول و یا تیرهای یک دهانه بودند، مدل مناسب‌تری باشد. گرچه با اضافه شدن دهانه‌ها و استفاده از معادله مشخصه ماتریس ضرایب برای به‌دست‌آوردن تابع شکل، بسیار دشوار خواهد شد. همچنین استخراج تابع فرکانس به کمک روش رایلی انجام شد و نتایج نشان داد که همچون روش حل مستقیم تاثیر عوامل روی مود اصلی سازه میزان خطای نتایج را تغییر می‌دهد. در این بخش با اضافه کردن جرم آزمون در نقاطی که روی مد اصلی متاثر است و در حل مستقیم تابع شکل در حالتی به دست می‌آید که جرم آزمون حضور ندارد و این موضوع باعث احتمال افزایش خطا با افزایش جرم آزمون را افزایش می‌دهد.

determining the amount of damage of two-span beams using rayleigh's method

in modern societies, the importance of financial and temporal resources is evident and has received attention inrecent decades, and it is predicted that such importance increases with time. structural health monitoring and crackdetection are two topics in the field of civil engineering, which two areas have a key role and is considered almostnew knowledge in civil engineering. in this project, we will try to use basic structural dynamics relations andstrength of materials to achieve a better understanding of structural damage. in fact, this project offers a practicalmethod that uses natural frequency to help identify the rate of damage to the support, which can help structuralimprovement. in this method, the only requirement is to obtain frequency from the structure and there is no need forstructural control and permanent presence of manpower. as you will see, dynamic parameters have a strong role inthis regard. what makes structural health and crack detection in particular both interesting and hard is significantuncertainty of structural damage. in fact, much uncertainty is involved in formation of structural damage and itsdetection and repair, which makes it a hard task with a high computational cost. despite all these problems, due toimportance of structural health monitoring and attempt to make most of available resources, many researches havebeen done in this regard and certainly the costs of knowledge of structural damage is much less than the material andnon-material damages of incidents in communities.although we studied a sample model of structure, given this discussion is newly emerged, this elementary modelwill be needed in future for much more complicated models that are closer to real structures. besides the above said,we saw in this project that despite study of damage to supports is very important in overall stability of structure andseems a difficult problem, a good knowledge of damage can be obtained using simple and reliable relations. thestructure studied in this project that had three damaged supports can provide a better model, compared to previousones, which were mostly in form of console or single-opening beams. however, addition of openings and use ofcharacteristic coefficients matrix equation to obtain shape function will be very hard and requires that we look for asimpler alternative method in this section. the other points of this project include direct study of level of damage.what has been sought so far rather in the area of damage detection includes an interpretation of the level of damagethrough variations of frequency or study of trend of variations of mode shape. in this project, having obtained thefrequency of damaged structure using the said method, we obtained level of stiffness reduction.as for direct solution, which is aimed to find proper shape function, acceptable results were obtained. but thetrend of results shows that error of this method increases as difference of stiffness of supports increases. it can beinferred that, given rayleigh’s opinion, difference of stiffness cause the main mode to take distance from the firstmode and such difference results in error. in fact, if stiffness of supports is symmetric, the main mode of thestructure, which unveils the main structure of the shape function, gets closer to the first mode, which makes theinitial assumption for shape function more acceptable.in the second part, which is derivation of frequency function with the aid of rayleigh method, as is the case withdirect solution method, the effect of factors of the main mode of structure changes the error level of the results. inthis part, by addition of test mass at points on the main mode. in direct solution, we obtained the shape function inabsence of test mass, which causes error to increase with test mass.