Dynamic Stability of Single Walled Carbon Nanotube Based on Nonlocal Strain Gradient Theory
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک
فرشید آقاداودی
1
(مربی
دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینیشهر)
محمد هاشمیان
2
(استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد خمینیشهر)
کلید واژه: Dynamic stability, Carbon Nanotube, Strain gradient, Euler-Bernouli beam, Non-local alasticity,
چکیده مقاله :
This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano- size structures such as single-walled carbon nanotubes. Influences of nonlocal effects, modulus parameter of elastic medium and aspect ratio of the SWCNT on the critical buckling loads and instability regions are analyzed. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanotubes.
در این مقاله پایداری دینامیکی نانولوله کربنی تک جداره به کمک تئوری غیرموضعی گرادیان کرنش مورد بررسی قرار گرفته است. پس از معرفی تئوری گرادیان کرنش و پایداری دینامیکی، نانولوله کربنی با استفاده از تیر اویلر- برنولی مدل شده و تحت بارگذاری استاتیکی و دینامیکی قرار گرفته است. محیط در بردارنده نانولوله بصورت الاستیک در نظر گرفته شده است. معادلات حرکت با استفاده از روش انرژی و اصل همیلتون استخراج شدهاند. با توجه به اینکه تئوریهای کلاسیک الاستیسیته در سازه با ابعاد نانو به طور کامل جوابگو نیست معادلات ساختاری ماده به کمک تئوری گرادیان کرنش استخراج شده و این معادلات به صورت غیرموضعی حل شده است. ارتعاشات آزاد و تحلیل کمانش استاتیکی انجام شده است. سپس تحلیل دینامیکی انجام شده و مرزهای پایداری در فرکانسها و دامنه های مختلف تعیین شدهاند. همچنین تأثیر عوامل مختلف بر این مناطق بررسی شده است.
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