بررسی نیمه تحلیلی ارتعاشات غیرخطی القائی ناشی از سیال در تیرهای ویسکوالاستیک با مدل جامد استاندارد با استفاده از روش‌‌ مقیاس‌های زمانی چندگانه

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار گروه مهندسی مکانیک، دانشکده فنی مهندسی مکانیک، دانشگاه گیلان، رشت، ایران

2 دانشکده مهندسی مکانیک-دانشگاه گیلان-رشت

چکیده

در این تحقیق رفتار ارتعاشات غیرخطی تیر اویلر-برنولی ویسکوالاستیک تحت تأثیر جریان سیال خارجی مطالعه شده است. معادلات حاکم بر حرکت با فرض روابط کرنش-جابجایی غیرخطی ون کارمن و در نظر گرفتن اندرکنش بین سازه و سیال به دست آمده است. به منظور در نظر گرفتن فرضیات واقع‌بینانه‌تر، اثر رفتار ویسکوالاستیک با استفاده از مدل کامل‌تر و واقع‌بینانه‌تر جامد استاندارد در نظر گرفته شده است. پس از بی‌بعدسازی معادلات حرکت، معادلات دیفرانسیل غیرخطی حاکم توسط روش گالرکین گسسته‌سازی شده و پاسخ تحلیلی سیستم با استفاده از روش مقیاس‌های زمانی چندگانه به دست آمده است. پس از صحت‌سنجی نتایج و تأیید دقت روش نیمه‌تحلیلی با نتایج حاصل از حل عددی، تأثیر پارامترهای مختلف بر رفتار دینامیکی سیستم مطالعه شده است. نتایج نشان می‌دهد رفتار ویسکوالاستیک و مدل غیرخطی تأثیر قابل ملاحظه‌ای بر ناحیه قفل‌شدگی و همچنین حداکثر دامنه نوسانات تیر ویسکوالاستیک دارد. با توجه به اینکه در اکثر مطالعات انجام شده در زمینه ارتعاشات تیرهای ویسکوالاستیک، اثر میرایی در جملات غیرخطی صرف‌نظر شده است، نتایج این تحقیق نشان می‌دهد که تأثیر میرایی بر جملات ناشی از غیرخطی بودن میدان‌های کرنش قابل ملاحظه بوده و این اثرات بایستی در استخراج معادلات حرکت حاکم بر رفتار ارتعاشاتی سازه‌های ویسکوالاستیک در نظر گرفته شود. 

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Semi-Analytical Study of Fluid-Induced Nonlinear Vibrations in Viscoelastic Beams with Standard Linear Solid Model Using Multiple Time Scales Method

نویسندگان [English]

  • Gholamreza Zarepour 1
  • Ilghar javanshir 2
1 Assistant Professor, Department of Mechanical engineering, Guilan University, Rasht, Iran,
2 PhD candidate, Department of Mechanical engineering, Guilan University, Rasht, Iran
چکیده [English]

In this research, the behavior of nonlinear vibrations of the viscoelastic Euler-Bernoulli beam under the influence of external fluid flow has been studied. The governing equations of motion are obtained by assuming Von-Karman nonlinear strain-displacement relations and considering the interaction between structure and fluid. To consider more realistic hypotheses, contrary to previous researches, the effect of viscoelastic behavior has been evaluated using a more complete and practical model called the Standard linear solid model. After non-dimensionalizing the motion equations, the governing nonlinear differential equations are discretized using the Galerkin method. Then, the system's analytical response is acquired through the method of multiple time scales. After verifying the results and confirming the semi-analytical method's accuracy with the numerical solution results, different parameters' effect on the system's dynamic behavior has been analyzed. The results indicate that the viscoelastic behavior and the nonlinear model significantly affect the lock-in area and the maximum amplitude of the viscoelastic beam vibrations. In most studies on viscoelastic beams' vibrations, the damping effect in nonlinear terms has been neglected. However, this study demonstrates that the effect of damping on terms related to the nonlinearity of strain fields is substantial.

کلیدواژه‌ها [English]

  • fluid-induced vibration
  • Fluid flow
  • Multiple time scales
  • Standard linear solid
  • viscoelastic beam
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