مطالعه پارامتریک ارتعاشات وابسته به‌اندازه تیرهای مدرج محوری رایلی تحت یک بار متحرک بر روی بستر پاسترناک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 مهندسی مکانیک، دانشکده مهندسی مکانیک، دانشگاه تربیت مدرس، تهران

2 تربیت مدرساستاد، دانشکده مکانیک، دانشگاه تربیت مدرس، تهران، ایران

چکیده

ارتعاشات میکروتیرهای مدرج تابعی محوری رایلی و اویلر برنولی تحت یک بار متحرک بر روی بستر پاسترناک به صورت عددی و تحلیلی مطالعه شده است. همچنین، برای اولین بار، یک مدل‌سازی دقیق ریاضی برای تحلیل اثر پارامترهای مختلف مانند گرادیان طولی مواد، فاکتور اینرسی دورانی، سختی بستر پاسترناک و پارامتر گرادیان کرنش بر سرعت بحرانی، ضریب دینامیکی و مکانیزم های لغو و ماکسیمم دامنه ارتعاشات سیستم به‌ دست ‌آمده است. فرکانس‌های طبیعی تیر مدرج تابعی محوری رایلی به ‌دست ‌آمده و با نتایج موجود در ادبیات فنی مقایسه می‌شوند. عبارت‌های ریاضی فرم بسته ساده برای ضریب بزرگنمایی دینامیکی، لغو و بیشینه دامنه ارتعاشات آزاد سیستم استخراج شدند. نشان داده می‌شود که به ازای مقادیر کمتر و بیشتر از پارامتر گرادیان بحرانی، تغییرات مشخصات مادی سیستم اثرات معکوس بر دامنه ارتعاش اجباری و آزاد سیستم دارند. علاوه بر این، نتیجه‌گیری می‌شود که در مقایسه با تیرهای اویلر- برنولی همگن، در میکروتیرهای مدرج محوری رایلی محاط شده در بستر برشی پاسترناک، با انتخاب مقادیر مناسبی از پارامتر گرادیان، ضریب اینرسی دورانی، سختی بستر و پارامتر گرادیان کرنش، می‌توان پدیده‌های لغو و بیشینه ارتعاشات آزاد سیستم را به‌خوبی کنترل کرد. همچنین نتایج پژوهش حاضر می‌تواند به‌عنوان معیاری برای طراحی بهینه سازه‌های ناهمگن تحت تحریک بارهای متحرک به‌کاربرده شوند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Parametric investigation of the size-dependent axially graded Rayleigh beams subjected to a moving load on Pasternak substrate

نویسندگان [English]

  • ali forooghi 1
  • mehran safarpour 1
  • akbar ali beigloo 2
1 Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
2 Department of mechanical engineering, Tarbiat modares university
چکیده [English]

The vibration of axially graded Rayleigh and Euler-Bernoulli micro-beams under a moving load on Pasternak foundation is studied numerically and analytically. Accurate mathematical modeling is acquired to analyze the effect of various parameters such as longitudinal gradient parameter of material, whirling inertia factor, the stiffness of Pasternak foundation, and strain gradient parameter on the critical velocity, and cancellation mechanism and the maximum amplitude of vibrations. Natural frequencies are obtained and compared with available results in the technical literature. Closed-form expressions are extracted for dynamic magnification coefficient and maximum amplitude of free vibration. The changes in material characteristics of the system have inverse influences on the amplitude of free and forced vibrations for lower and higher values of the critical gradient parameters. It is concluded that in comparison with homogenous Euler-Bernoulli beams, in the axially graded Rayleigh micro-beams surrounded by shear Pasternak foundation. It can be controlled the cancellation and maximum free vibration phenomenon, by choosing the accurate values of gradient parameter, whirling inertia coefficient, the stiffness of foundation, and strain gradient parameter. Also, the results of the present study can be used as a criterion for the optimal design of heterogeneous structures under the moving loads.

کلیدواژه‌ها [English]

  • Moving load
  • Axially graded material
  • cancellation phenomenon
  • Maximum amplitude of vibrations
  • Critical velocity of loading
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