بررسی تأثیر شرایط مرزی مرتبه بالا بر ارتعاشات آزاد ریزپوسته‌‌های ضخیم مخروطی مدرج تابعی دوجهته

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی مکانیک، دانشگاه حکیم سبزواری

چکیده

پژوهش پیش‌‌رو تأثیر شرایط مرزی مرتبه بالای ناشی از در نظر گرفتن اثر ابعاد کوچک را بر ارتعاشات آزاد ریزپوسته‌‌های ضخیم مخروطی مدرج تابعی دوجهته بررسی می‌‌کند. مدل حاضر تغییرات پارامتر مقیاس طول مادی را به‌‌عنوان یکی از خواص مکانیکی ریزپوسته در راستای ضخامت و همچنین در امتداد محور طولی آن مد نظر قرار می‌‌دهد. تئوری‌‌های‌‌ تنش‌‌کوپل بهبود یافته و پوسته لاو با در نظر گرفتن تغییر شکل‌‌های برشی مرتبه اول به‌‌همراه روش ریتز به‌‌خدمت گرفته می‌‌شوند تا معادلات مقدار ویژه - بردار ویژه حاکم بر ارتعاشات آزاد ریز سازه تعیین شوند. این معادلات برای چند شرط مرزی مختلف حل می‌‌گردند. نتایج حاضر با نتایج موجود در مقالات مرتبط مقایسه و به‌‌صورت موفقیت‌‌آمیزی صحه‌‌گذاری می‌‌شوند. سپس اثرات ابعاد کوچک، شرایط مرزی مرتبه بالا و اندیس‌‌های تابع توزیع توانی در هر دو راستای عرضی و طولی بر ارتعاشات آزاد ریزپوسته‌‌های مخروطی شکل مورد بررسی قرار می‌‌گیرند. نتایج حاکی از آنند که شرایط مرزی مرتبه بالا نقشی حیاتی در دینامیک ریزپوسته مخروطی بازی می‌‌کنند؛ خصوصاً هنگامی‌‌که این شرایط مرزی مودهای غالب در دینامیک سازه را مستقیماً تحت تأثیر قرار می‌‌دهند. همچنین مشاهده گردید اگرچه دینامیک ریزپوسته مخروطی حاضر از اندیس‌‌های تابع توزیع توانی در هر دو راستای عرضی و طولی تحت تأثیر می‌‌پذیرد، اما حساسیت بیشتری نسبت به اندیس عرضی دارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Investigating the Influence of Higher-Order Boundary Conditions on Free Vibrations of Bi-Directional Functionally Graded Thick Conical Micro-Shells

نویسندگان [English]

  • Mohsen Taghizadeh
  • Amir Reza Askari
Department of Mechanical Engineering, Hakim Sabzevari University
چکیده [English]

The present paper investigates the influence of higher-order boundary conditions caused by accounting for the small scales effect on free vibrations of bi-directional functionally graded thick conical micro-shells. The present model accounts for the gradation of the material length scale parameter as one of the micro-shell mechanical properties along with its thickness as well as its axial axis. The modified couple stress as well as the first-order shear deformable love shell theories together with the Ritz method are employed to obtain the eigenvalue eigenvector equations governing the free vibrations of the microstructure. These equations are solved for some different types of boundary conditions. The present findings are compared and successfully validated by the available results in the literature. The influences of small scales, higher-order boundary conditions, and power-law distribution indices in both the transversal and axial directions on free vibrations of conical micro-shells are then investigated. The results reveal that higher-order boundary conditions play a crucial role in the dynamics of conical micro-shells especially when these boundary conditions directly affect the eigenmodes which are dominant in the dynamics of the structure. In addition, it is observed that although the dynamics of the present conical micro-shell is affected by the power-law distribution indices in both the transversal and axial directions, it is more sensitive to the transversal one.

کلیدواژه‌ها [English]

  • Modified Couple Stress Theory
  • Conical micro-shells
  • Bi-directional functionally graded materials
  • Higher-order boundary conditions
  • The Ritz method
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