ارتعاشات غیرخطی پیچشی تیر با نیروی محوری و دارای زاویه پیچش اولیه تحت تحریک تشدید اصلی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 صنعتی شاهرود-مهندسی مکانیک

2 دانشگاه صنعتی شریف، دانشکده مهندسی هوافضا

چکیده

در این مقاله، ارتعاشات غیرخطی پیچشی تیر در شرایط تحریک تشدید اصلی مورد بررسی قرار گرفته است. در معادلات غیرخطی حاکم بر حرکت، اثرات مربوط به قید اعوجاج و زاویه پیچش اولیه و نیروی محوری و اینرسی پیچشی در نظر گرفته شده است. وجود همزمان نیروی محوری و زاویه پیچش اولیه منجر به پدیده واپیچش می‌شود. معادلات غیرخطی بی‌بعد شده حاکم بر ارتعاشات پیچشی تیر در شرایط تشدید اصلی با استفاده از روش اغتشاشی مقیاس‌های چندگانه به ازای شرایط مرزی مختلف حل شده است. تشدید اصلی مود اول و مود دوم به صورت جداگانه مورد بررسی قرار گرفته است. حل تحلیلی برای پاسخ پیچشی تیر در حالتهای مختلف تحریک ارائه گردیده است. بررسی پاسخ‌ها نشانگر ظهور هارمونیک‌هایی علاوه بر هارمونیک اصلی در پاسخ است. علاوه بر این، تحلیل معادلات حاکم نشان می‌دهد که مسئله در پاره‌ای شرایط شامل پدیده تشدید داخلی سه به یک هست. معادلات دامنه پاسخ و فاز به ازای شرایط تشدید مختلف ارائه و نتایج عددی مرتبط نیز ذکر گردیده است. پایداری جواب‌ها، اندرکنش بین مودها و امکان انتقال انرژی بین مودهای ارتعاشی به صورت ویژه مورد بررسی قرار گرفته است. نتایج ارائه شده موید اهمیت پدیده‌های غیرخطی در ارتعاشات پیچشی تیر است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlinear Torsional Vibrations of Axially Loaded Pretwisted Beam with Primary Resonance Excitations

نویسندگان [English]

  • Seyed Ali Sina 1
  • Hassan Haddadpour 2
1 صنعتی شاهرود-مهندسی مکانیک
2 Dept. of Aerospace Engineering, Sharif Univ. of Tech.
چکیده [English]

Frequently used thin walled beams have low torsional stiffness and their torsional deformations may be of such magnitudes that it is not adequate to treat the angles of cross section rotation as small. In this paper, nonlinear torsional vibrations of thin walled beams will be investigated. The method of multiple scales will be implemented as a solution method and different nonlinear phenomena will be studied. The obtained results are compared with the available results in the literature which reveals an excellent agreement between different solution methodologies. The outcomes of this study show that beam nonlinear torsional dynamics and the related phenomena could influence the linear torsional dynamic of beams under axial load, e.g. rotating beams. Forced torsional vibrations of a beam with the excitation in the form of primary resonance of the first and second modes have been investigated. It has been demonstrated that in the case of the beam with two ends clamped boundary conditions, three-to-one internal resonance will appear. The primary resonance of the first and second modes has been solved in two sets of boundary conditions, torsionally clamped-fixed and torsionally fixed-fixed. Nonlinear response, amplitude-phase equations, fixed points, and their stability have been studied.

کلیدواژه‌ها [English]

  • Beam torsional vibration
  • Nonlinear vibration
  • Pretwist angle
  • Axial load
  • Primary resonance
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