بررسی رفتار دینامیکی و پایداری میکروتیرهای متحرک با خواص مدرج تابعی در جهت طولی

نوع مقاله: مقاله مستقل

نویسندگان

1 دانشجوی کارشناسی ارشد، مهندسی مکانیک، دانشگاه تربیت مدرس، تهران

2 استاد، مهندسی مکانیک، دانشگاه تربیت مدرس، تهران

10.22044/jsfm.2020.8952.3027

چکیده

باهدف بهبود کارایی سامانه‌های متحرک محوری، ارتعاشات و پایداری میکروتیرهای رایلی مدرج محوری با حرکت طولی در این مقاله مطالعه شده است. همچنین، یک مطالعه پارامتریک مفصل برای توضیح اثر پارامترهای مختلف مانند درجه‌بندی محوری مواد، طول مشخصه ماده 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. با به‌کارگیری تئوری گرادیان کرنش و روش گسسته‌سازی گالرکین، مسئله مقدار ویژه برای سیستم حل شده است 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 قرار گفته‌اند. نتایج نشان می‌دهند در حالت چگالی و مدول الاستیک متغیر، به ترتیب تغییرات نمایی و خطی منجر به سیستم پایدارتر می‌شوند. همچنین 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.

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