تحلیل ناپایداری الاستیک و ارتعاش آزاد تیر تیموشنکو ساخته ‌شده از مواد مدرج تابعی با مقطع متغیر

نوع مقاله : علمی - پژوهشی

نویسندگان

1 گروه مهندسی عمران، دانشکده مهندسی، دانشگاه کاشان، کاشان، ایران

2 عمران- خواجه نصیر الدین طوسی

3 گروه مهندسی عمران، دانشگاه کاشان ،کاشان، ایران

چکیده

در این پژوهش، رفتار پایداری و ارتعاش آزاد تیر تیموشنکو غیرمنشوری ساخته شده از مصالح مدرج تابعی (FGM) مورد مطالعه قرار گرفته است. ترکیب خصوصیات اعضای غیرمنشوری و مصالح مدرج تابعی باعث استفاده بهینه از تمام ظرفیت مقطع، کاهش چشمگیر وزن سازه و درنهایت سبب ایجاد بهترین حالت طراحی برای سیستم‌های ارتجاعی می‌شود. همچنین، تعیین فرکانس طبیعی ارتعاش اعضای سازه‌ای در تحلیل مسائل دینامیکی از اهمیت ویژه‌ای برخوردار است. از سوی دیگر مسئله پایداری یکی از معیارهای اصلی طراحی اعضا است. بنابراین، در این پژوهش با استفاده از روش تفاضل محدود پیش رو، مرکزی و پس رو با دقت مرتبه دو، فرکانس طبیعی ارتعاش و بار کمانش بحرانی تیر تیموشنکو غیرمنشوری ساخته ‌شده از مصالح مدرج تابعی با در نظر گرفتن سه نوع شرایط مرزی: دو سر گیردار، یک سر گیردار- یک سر آزاد و دو سر مفصلی تعیین شده است. خصوصیات مصالح در راستای طولی به‌صورت پیوسته و براساس قانون توزیع توانی تغییر می‌کند. درحالی‌که؛ خواص مواد در راستای ضخامت تیر ثابت و بدون تغییر باقی می‌ماند. همچنین به علت تغییر اندک ضریب پوآسون مصالح در طول تیر، مقدار آن ثابت در نظر گرفته شده است. در انتها با مقایسه نتایج حاصل با نتایج مقاله‌های معتبر و همچنین مقادیر حاصل از نرم افزار آباکوس، صحت و دقت روش مذکور تایید شده است. همچنین، تاثیر عوامل مختلفی مانند توان ماده مدرج تابعی، ضریب باریک شوندگی مقطع و نوع تکیه‌گاه بر بار کمانش بحرانی و فرکانس طبیعی ارتعاش تیر ماهیچه‌ای به تفصیل مورد مطالعه قرار گرفته است و نشان داده شد که توان ماده تابعی تاثیر عمده‌ای بر رفتار پایداری و ارتعاشی تیر ماهیچه‌ای می‌گذارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Elastic instability and free vibration analyses of axially functionally graded Timoshenko beams with variable cross-section

نویسندگان [English]

  • Masoumeh Soltani 1
  • Behrouz Asgarian 2
  • Vahid jafari Deligani 3
1 Department of civil engineering, Faculty of engineering, University of Kashan, Kashan, Iran
2 Faculty of civil engineering, K.N. Toosi University of Technology, Tehran, Iran
3 Department of civil engineering, Faculty of engineering, University of Kashan, Kashan, Iran
چکیده [English]

In this paper, the critical buckling loads and natural frequencies of axially functionally graded non-prismatic Timoshenko beam with different boundary conditions are acquired using the Finite Difference Method (FDM). In the recent years, the use of functionally graded materials (FGMs) has been increasing in different mechanical components due to their conspicuous characteristics such as high strength, thermal resistance and optimal distribution of weight. The designer can thus produce structures with favorable stability and manage the distribution of material properties. In this study, the material properties of non-prismatic Timoshenko beams such as Young’s modulus of elasticity and density of material are described by a power-law formulation along the beam axis. Contemplating elastic behavior, the system of equilibrium equations of non-uniform Timoshenko beam and the related boundary conditions are coupled in terms of the vertical displacement and the bending rotation of the cross-section. Afterwards, the system of second-order differential equations with variable coefficients and end conditions are discretized by finite difference formulations with second-order accuracy. Finally, the system of finite difference equations culminates in a set of simultaneous and linear equations and the critical buckling loads and natural frequencies are calculated by solving an eigenvalue problem of the obtained algebraic system. In order to demonstrate the accuracy and reliability of this approach to calculate elastic buckling loads and natural frequencies of functionally graded (FG) Timoshenko beams, one comprehensive example including axially non-homogeneous and homogeneous members with non-uniform cross-section is expressed. The numerical results in clamped-clamped, simply supported and fixed-free boundary conditions are accomplished. Moreover, the effect of various parameters such as volume fraction index, end conditions and the section variation on the elastic buckling and free vibration behavior of AFG Timoshenko beam are investigated in detail.

کلیدواژه‌ها [English]

  • Tapered Timoshenko Beam
  • Axially Functionally Graded Material
  • Natural Frequency
  • Critical buckling load
  • Finite difference method
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