ارتعاشات غیرمحلی نانوتیر محاط شده در بستر ویسکوالاستیک-پاسترناک با حرکات طولی و چرخشی با درنظرگیری اثرات سطحی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشگاه تربیت مدرس، تهران، ایران

چکیده

در این پژوهش، ارتعاشات وابسته به‌اندازه تیرهای نانومقیاس که به‌صورت هم‌زمان دارای حرکات طولی و چرخشی هستند، براساس تئوری غیرمحلی ارینگن تحلیل شده است. همچنین، برای اولین بار، یک مطالعه پارامتریک برای توضیح اثرات سطحی، مشخصات بسترهای ویسکوالاستیک-پاسترناک، ویژگی‌های هندسی، بارهای حرارتی، سطح مقطع‌های متقارن و نامتقارن، نیروهای محوری و پیرو بر دینامیک و پایداری سیستم بررسی شده است. ابتدا معادلات دینامیکی سیستم با به‌کارگیری اصل همیلتون استخراج می‌شوند. سپس با کمک روش گسسته‌سازی گالرکین، فرکانس‌های طبیعی سیستم تعیین می‌شوند. برای اطمینان از صحت مدل و روش حل ارائه‌شده، نتایج پژوهش حاضر با نتایج مقالات منتشرشده مقایسه و اعتبارسنجی شدند. نقشه‌های پایداری و دیاگرام کمپل به ازای شرایط مختلف کاری رسم شدند. نتایج نشان دادند که با افزایش مدول الاستیسیته و تنش پسماند سطحی، فرکانس‌های ارتعاشاتی و آستانه ناپایداری دینامیکی سیستم افزایش می‌یابند. همچنین، با افزایش ضخامت/طول سیستم، سرعت محوری ناپایداری استاتیکی کاهش/افزایش می‌یابد. ضمناً، مشاهده شده است که برعکس اثرات غیرمحلیت، با افزایش ضرایب الاستیک و برشی بستر عملکرد سیستم بهبود می‌یابد. نتایج تحقیق حاضر کمک قابل‌توجهی به طراحان و مهندسان در کنترل ارتعاشات نانوسازه‌های بایژیروسکوپیک خواهند کرد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlocal Vibration of Nanobeam Embedded in Viscoelastic Pasternak Foundation with Longitudinal and Rotational Motions with Surface Effects

نویسندگان [English]

  • Omid Koochakianfard
  • Akbar Alibeigloo
Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran
چکیده [English]

This paper analyzes the size-dependent vibration of nanoscale beams with simultaneously longitudinal and rotational motions based on nonlocal theory for the optimum design of nanoscale surgical robots. Also, for the first time, a parametric study is performed to explain the surface effects, viscoelastic-Pasternak foundations characteristics, thermal loads, geometric properties, symmetric and asymmetric cross-sections, axial and follower loads on the dynamics and stability of the system. Adopting the Galerkin discretization approach, the reduced-order dynamic model of the system is acquired. Also, analytical and numerical methods are exploited. To ensure the accuracy of the proposed model and method, the present study results are compared and validated with those of published articles. Stability maps and Campbell diagrams are drawn for different working conditions. The results showed that increasing the surface elastic modulus and residual stress improves the vibration frequencies and dynamic instability threshold. It is also found that with increasing system thickness/length, the axial velocity of static instability decreases/increases. In addition, it is observed that the system performance improves with increasing the elastic and shear coefficients of the foundation. The results of the present study significantly help designers and engineers control the vibration of bi-gyroscopic nanoscale robots.

کلیدواژه‌ها [English]

  • Nanobeam
  • longitudinal and rotational motions
  • Vibration frequency
  • Nanoscale surgical robots
  • Surface effects
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