تحليل لرزه‌‌اي مخازن ذخيره سيال مجهز به تيغه ميراگر حلقوي با استفاده از روش المان مرزي

Seismic Analysis of Baffled Liquid Storage Tanks Using Boundary Element Method

چكيده- اهميت مخازن ذخيره سيال در زندگي امروزه به اندازه سيالاتي است كه در زندگي شهري مورد استفاده قرار مي‌گيرند. مطالعات گوناگوني بر روي اين سازه هاي تاثيرگذار انجام شده است كه از جمله اين مطالعات تاثير سيستم هاي كنترل بر پاسخ لرزه‌اي مخزن است. از ميان سيستم هاي مزبور، تيغه هاي ميراگر به عنوان يكي از ابزارهاي كنترل غيرفعال با هدف كاهش تاثير امواج تلاطمي بر پاسخ مخازن ذخيره سيال مطرح است. در اين پژوهش، تاثير تيغه‌هاي ميراگر حلقوي شكل، كه در ارتفاع معيني از كف مخازن زميني استوانه اي نصب شده است، بررسي مي‌شود. با در نظر گرفتن معادله لاپلاس به عنوان رابطه حاكم بر رفتار سيال و با استفاده از روش المان مرزي، آناليز مخزن صلب در قلمرو فركانس و زمان انجام شده است. سپس تاثير تيغه ميراگر بر فركانس مود طبيعي (در قلمرو فركانس) و برش پايه و لنگر واژگوني (در قلمرو زمان) تحت زلزله هاي ارزينكان و ال‌سنترو بررسي شده است. بر اساس نتايج حاصل از آناليزهاي مزبور، ملاحظه مي شود كه با قراردادن تيغه شاهد كاهش فركانس مود طبيعي خواهيم بود. همچنين، تاثير تيغه بر پاسخ تحريك ناشي از دو شتاب‌نگاشت يادشده به صورت افزايش ناچيز برش پايه و كاهش چشمگير لنگر واژگوني بوده است.

Abstract: Nowadays, fluid storage tanks play critical role as lifeline facilities which are as important as fluidsʹ supplement in urban life. The dynamic behavior of these vital structures is different from common structures. In order to protect these structures against destructive effects of seismic loading, various active and passive devices may be employed. Baffles as passive control devices can reduce the effects of sloshing, which in turn reduces the structural response to seismic excitations. In this study, the effect of baffles on the seismic response of cylindrical vertical liquid storage tanks is investigated. The considered baffle is an annular plate with constant level from the base and constant inner diameter. The baffle is fixed on the wall of the tank. Fluid motion is assumed to be irrotational, incompressible and inviscid. Therefore, considering Laplaceʹs equation as the governing equation of the fluid domain, and using boundary element method, a rigid tank is analyzed. In this study, both frequency and time domains are taken into account. In the frequency domain, the baffle effects on natural frequency are studied, while in the time domain, the baffle effects on the base shear and overturning moment are investigated. In order to develop an efficient numerical tool based on boundary element method, the well-known substructuring approach is implemented in this research. For this purpose, the fluid domain is divided into two upper and lower potions partitioned by the baffle. As a result, the compatibility boundary conditions should be satisfied at top and bottom sides of baffle which interact with the fluid domain. Furthermore, continuity boundary condition is fulfilled at the common boundary of two portions of the fluid domain. Linearized free surface condition is taken into consideration. By discretizing the fluid boundaries to quadrilateral elements, the boundary integral equation is formulated into a general matrix form. This general matrix form is then reduced to a more efficient form, which reduces the size of the computational matrices considerably. The result obtained using the present method is verified in comparison with the results available in the literature, with very good agreement. Finally, some example tanks are used to study the baffleʹs effect on the responses of the example tanks excited by El Centro and Erzincan earthquakes. Based on the results obtained by of mentioned analyses, it is observed that when the baffle is installed, the natural frequency of liquid domain reduces. Moreover, by installing the baffle, the base shear slightly increases whereas overturning moment remarkably reduces. These promising results encourage the authors to follow the present research for the case of flexible baffles, in which the fluid-structure interaction may play a crucial role.