IJE TRANSACTIONS B: Applications Vol. 28, No. 2 (February 2015) 296-304   

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Y. Tadi Beni, A. Jafaria and H. Razavi
( Received: August 14, 2014 – Accepted: November 13, 2014 )

Abstract    In this paper, the transverse vibration of cracked nano-beam has been studied based on modified couple stress theory. Crack is modeled by a rotational spring that creates a discontinuity. Frequency equations of cracked nano-beam with some typical boundary conditions are derived and the frequency parameter for different crack positions, crack parameter and length scale parameters value are calculated. According to the results, it can be found that the effects of the crack parameter and crack location on transverse frequency of the cracked nano-beam are significant. In addition, scale effect parameter is one of the important parameter in nanoscale that must be obtained. Finally, the results of special cases show good agreement with the results available in the literature.


Keywords    Cracked nano-beam, frequency parameter, couple stress theory, size effect parameter


چکیده    در این مقاله ارتعاشات عرضی نانوتیر ترک­دار با استفاده از تئوری تنش کوپل مورد مطالعه قرار گرفته­است. در اینجا ترک توسط دو فنر پیچشی و خطی مدل شده ­است که یک ناپیوستگی در تیر ایجاد می­کند. ابتدا معادله فرکانس عرضی نانو تیر ترک دار استخراج شده ­است و سپس فرکانس­های عرضی آن برای محل­های مختلف ترک، طول­های مختلف تیر، پارامتر اثر اندازه مختلف، مشخصات متفاوت ترک و شرايط مرزی مختلف نانو تير محاسبه گردیده­است. با توجه به نتايج می­توان گفت تاثیر سختی ترک و محل قرارگیری ترک بر مقادیر فرکانس­ها کاملا قابل توجه است و فرکانس­ها با افزایش مشخصات ترک کاهش می­یابند. در ضمن اثر اندازه يکی از پارامترهای مهم در مقياس نانو می­باشد که بايد مورد توجه قرار گيرد. در این مقاله به رابطه­ی بین شکل مود ارتعاشی تیرها و تغییرات فرکانس نانو تیر ترک دار نیز پرداخته شده­است. همچنین نتایج بدست آمده با نتایج کارهای مشابه در تئوری‌های کلاسیک، غیر موضعی و نتايج تجربی موجود در مراجع مقايسه شده است.


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