مطالعه تأثیر گرادیان طولی مواد بر ارتعاشات سیستم‌های متحرک محوری

نوع مقاله : مقاله پژوهشی

نویسندگان

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

چکیده

برای اولین بار، ارتعاشات و پایداری تیرهای رایلی متحرک مدرج محوری با هدف بهبود کارایی سیستم‌های متحرک عبوری مطالعه شده است. همچنین، یک مطالعه مقایسه‌ای مفصل برای روشن‌کردن اثر پارامترهای مختلف مانند درجه‌بندی محوری مواد و اینرسی دورانی بر مرزهای پایداری تیرهای رایلی و اویلر- برنولی انجام شده است. فرض شده است که مشخصات مادی سیستم به‌طور پیوسته در راستای طولی به‌صورت خطی یا نمایی تغییر می‌کنند. روش گسسته‌سازی گالرکین و همچنین مسئله مقدار ویژه به‌کاربرده شده‌اند تا فرکانس‌های طبیعی، پیکربندی دینامیکی، آستانه‌های ناپایداری فلاتر و دایورژانس سیستم محاسبه شوند. همچنین روابط تحلیلی برای سرعت بحرانی سیستم به‌دست‌آمده‌اند. نقشه‌های پایداری و کانتورهای سرعت بحرانی برحسب توزیع‌های مختلف مورد آزمون قرارگفته‌اند. ضمنا نشان داده شد که در حالت چگالی و مدول الاستیک متغیر، به ترتیب تغییرات نمایی و خطی منجر به سیستم پایدارتر می‌شوند. همچنین نتایج نشان دادند که کاهش پارامتر گرادیان چگالی و یا افزایش پارامتر گرادیان مدول الاستیک، فرکانس طبیعی سیستم را افزایش می‌دهد و محدوده‌های پایداری را گسترش می‌دهد، بنابراین تغییرات پارامترهای گرادیان چگالی و مدول الاستیک، نقش‌های متضاد در رفتار دینامیکی سیستم دارند. نتایج پژوهش حاضر برای طراحی و بهینه‌سازی سازه‌های متحرک محوری غیرهمگن سرعت بالا می‌تواند مفید باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Investigation of the effect of longitudinal grading of material on vibrations of axially moving systems

نویسندگان [English]

  • ali forooghi
  • mehran safarpour
  • akbar ali beigloo
Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran
چکیده [English]

For the first time, vibrations of the axially graded Rayleigh moving beams are studied. It is supposed that the material characteristics of the system change linearly or exponentially in a longitudinal direction continuously. By using the Galerkin method and eigenvalue problem, the natural frequencies and divergence of the system are computed numerically. Also, the analytical relations are extracted for the critical velocity of the system. Essential contours of velocity and stability maps are investigated for different distributions of material. As indicated, exponential and linear changes lead to more stable operation in the variable state of density and elastic modulus, respectively. Also, the results showed that increasing the elastic modulus gradient parameter or decreasing the density gradient parameter results in an increase in the natural frequency of the system and a development in stability. Hence, alteration in the density and elastic modulus gradient parameters has a different role in the dynamic behavior of the system. The results of this study can be useful for designing and optimizing high-speed non-homogeneous axial movable structures.

کلیدواژه‌ها [English]

  • Axial graded materials
  • Gradient parameter
  • Moving beam
  • Critical Velocity
  • Instability
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