Mamandi, A., Kargarnovin, M. (2012). Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 5(2), 61-72.
A. Mamandi; M.H. Kargarnovin. "Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force". Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 5, 2, 2012, 61-72.
Mamandi, A., Kargarnovin, M. (2012). 'Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force', Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 5(2), pp. 61-72.
Mamandi, A., Kargarnovin, M. Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 2012; 5(2): 61-72.
Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force
1Assistant Professor, Mechanical and Aerospace Engineering, Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Tehran, Iran.
2Professor, Mechanical Engineering, Department of Mechanical Engineering, Sharif university of Technology, Tehran, Iran
Abstract
This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time Scales. Under three to-one-internal resonance condition applying nonlinear normal modes the steady state stability analysis of the beam’s vibrations is performed. Then the effect of changing the value of different parameters on the beam’s dynamic response and the steady state stability analysis is investigated.
تحلیل ارتعاشات غیرخطی تیر اویلر برنولی بر روی بستر الاستیک غیرخطی تحت تأثیر بار محوری فشاری
Authors [Persian]
احمد مامندی1; محمدحسین کارگرنوین2
1استادیار، دکترای مهندسی هوافضا، دانشکده مهندسی مکانیک، واحد پرند، دانشگاه آزاد اسلامی، تهران، ایران
2استاد، دانشکده مهندسی مکانیک، دانشگاه صنعتی شریف، تهران، ایران
Abstract [Persian]
در این مقاله، ارتعاشات تیر اویلر- برنولی با در نظر گرفتن بستر الاستیک غیرخطی، بررسی شده است. تیر تحت بارگذاری محوری فشاری بوده و شرایط تکیهگاهی، مفصلی- غلطکی میباشد. تحلیل ارتعاشات بر اساس مدهای نرمال غیرخطی در وضعیت رزونانس داخلی سه به یک (3:1) انجام می‌گیرد. معادلهی دیفرانسیلی غیرخطی حاکم بر ارتعاشات عرضی تیر استخراج شده و به کمک روش چند مقیاس زمانی، تحلیل شده است. در وضعیت رزونانس داخلی 3:1 بر اساس مدهای نرمال غیرخطی در حالت پایا، پایداری پاسخ فرکانسی ارتعاشات غیرخطی تیر مطالعه شده، سپس تأثیر تغییر پارامترهای مختلف بر روی نتایج تحلیل دینامیکی و تحلیل پایداری پاسخ فرکانسی ارتعاشات غیرخطی تیر بررسی شده‌است.
Keywords [Persian]
ارتعاشات غیرخطی، تیر اویلر برنولی، بستر الاستیک غیرخطی، رزونانس داخلی سه به یک، تحلیل پایداری حالت پایا
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