تحلیل ارتعاش آزاد غیرخطی ورق‌های مستطیلی از جنس ماده مدرج تابعی دوجهته

نوع مقاله: مقاله مستقل

نویسندگان

1 کارشناسی ارشد، دانشکده مهندسی مکانیک، دانشگاه خواجه‌ نصیرالدین طوسی، تهران

2 استاد، دانشکده مهندسی مکانیک، دانشگاه خواجه‌ نصیرالدین طوسی، تهران

10.22044/jsfm.2020.9012.3046

چکیده

در تحقیق حاضر، ارتعاش آزاد غیرخطی ورق مستطیلی دورمفصل از جنس مواد مدرج تابعی دوجهته برای اولین بار به‌صورت کاملا تحلیلی بررسی شده‌است. برای این منظور به کمک اصل هامیلتون و روابط کرنش جابجایی غیرخطی ون‌کارمن، معادلات دیفرانسیل جزئی حرکت ورق استخراج شده‌اند. پس از آن با اعمال روش گالرکین، معادلات دیفرانسیل جزئی غیرخطی ورق به معادلات دیفرانسیل معمولی غیرخطی وابسته به زمان تبدیل گشته‌اند. سپس به منظور محاسبه فرکانس‌های غیرخطی ورق، معادله غیرخطی ورق به‌صورت تحلیلی با استفاده از روش لیندشتد پوانکاره بهبودیافته حل شده‌است. خواص مواد ورق براساس مدل توزیع توانی در دوراستای طولی و عرضی ورق به‌صورت پیوسته متغیر فرض شده‌اند. درنهایت اثر برخی پارامترهای کلیدی سیستم همچون دامنه ارتعاش، اندیس ماده مدرج تابعی و نسبت هندسی ورق بر روی فرکانس غیرخطی ورق به صورت جزئی مورد تحلیل قرار گرفته‌اند. برای صحه‌گذاری مساله، نتایج این پژوهش با نتایج ادبیات گذشته و همچنین حل عددی مقایسه شده‌است و تطابق بسیارخوبی مشاهده گشته‌است.

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