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تحلیل ارتعاش آزاد و پایداری خمشی-پیچشی تیر جدار نازک ماهیچه‌ای ساخته‌شده از مواد مدرج تابعی بر بستر الاستیک | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 10، دوره 53، شماره 6، شهریور 1400، صفحه 3587-3614 اصل مقاله (3.49 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2021.18445.6816 | ||
| نویسندگان | ||
| معصومه سلطانی* 1؛ علی آهنیان2 | ||
| 1گروه مهندسی عمران، دانشکده مهندسی، دانشگاه کاشان، کاشان، ایران | ||
| 2گروه مهندسی عمران، دانشکده مهندسی، دانشگاه کاشان، ایران | ||
| چکیده | ||
| مواد مدرج تابعی، مصالحی نوین با ساختاری ناهمگن و ویژگی‌های منحصر به فرد هستند که در سال‌های اخیر نظر پژوهشگران زیادی را به خود جلب کرده‌اند. بنابراین در این مقاله برای اولین بار، ارتعاشات آزاد و پایداری تیر ماهیچه‌ای با مقطع جدار نازک ساخته‌شده از مواد مدرج تابعی محوری بر بستر الاستیک وینکلر مورد بررسی قرار می‌گیرد. فرض بر این است که خواص مکانیکی ماده (ضریب ارتجاعی و چگال) در راستای طول عضو به‌طور پیوسته و براساس توزیع توانی، متغیر و نسبت پواسون ثابت فرض شده است. معادلات حاکم بر حرکت و شرایط مرزی با استفاده از اصل همیلتون و روش انرژی به‌دست می‌آیند. تحلیل پایداری و ارتعاش آزاد بر پایه مدل ولاسو برای مقاطع جدار نازک باز و با اعمال اثرات محل اتصال بستر الاستیک و خروج از مرکزیت بار فشاری در معادلات انجام شده است. با استفاده از روش مربعات دیفرانسیلی، دستگاه معادلات گسسته و حل می‌گردد. سپس با اعمال شرایط مرزی روی پاسخ‌های به‌دست‌آمده و با استفاده از روش حل مقادیر ویژه، بار کمانشی و فرکانس ارتعاشی محاسبه می‌شوند. در پایان نتایج حاصل از این تحقیقدر خصوص تیر همگن با مقطع متغیر با نتایج دیگر تحقیقات جهت بررسی صحت و دقت محاسبات مقایسه گردیده و تاثیر پارامترهای مختلفی همچون طول عضو، شرایط مرزی، خروج از مرکزیت بار فشاری، تغییر ابعاد مقطع، توان ماده مدرج تابعی، سفتی بستر الاستیک و محل اتصال فنر وینکلر بر روی پایداری و ارتعاش آزاد مورد ارزیابی قرار گرفته است. | ||
| کلیدواژه‌ها | ||
| کمانش خمشی-پیچشی؛ فرکانس ارتعاشی؛ مواد مدرج تابعی؛ بستر وینکلر؛ روش مربعات دیفرانسیلی | ||
| عنوان مقاله [English] | ||
| Free vibration and flexural-torsional stability analyses of axially functionally graded tapered thin-walled beam resting on elastic foundation | ||
| نویسندگان [English] | ||
| Masoumeh Soltani1؛ Ali Ahanian2 | ||
| 1Department of Civil Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran | ||
| 2Department of Civil Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran | ||
| چکیده [English] | ||
| The thin-walled beams are widely adopted in different structural components ranging from civil engineering to aeronautical applications due to their conspicuous characteristics. A slender thin-walled beam loaded initially in compression may buckle suddenly in flexural–torsional mode since its torsional strength is much smaller than bending resistance. In this paper, flexural-torsional stability and free vibration analyses of axially functionally graded tapered I-beam resting on Winkler elastic foundation are assessed. Considering the coupling between the flexural displacements and the twist angle, the motion equations are derived via Hamilton’s principle in association with Vlasov’s thin-walled beam theory. The differential quadrature method is applied to solve the system of differential equations and to acquire the critical buckling loads and natural frequencies. To validate the obtained results, at first, homogeneous tapered I-beam in the absence of elastic foundation was analyzed and compared with a finite element solution using ANSYS and other available benchmarks. Afterward, the numerical outcomes for axially graded non-prismatic I-beam resting on elastic foundation are reported in graphical form to find out the impacts of axial load position, beam’s length, end conditions, web and flanges tapering ratio, material gradient index, Winkler parameter and spring position on the non-dimensional buckling loads and vibration frequencies. | ||
| کلیدواژه‌ها [English] | ||
| Flexural-torsional buckling, Vibration frequency, Functionally graded materials, Winkler foundation, Differential quadrature method | ||
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| مراجع | ||
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