پوستههای استوانهای تقویتشده، یکی از مهمترین سازهها در صنایع هوافضا میباشند. در این مقاله یک روش نیمه تحلیلی برای تحلیل پوستههای استوانهای مدرج تابعی تقویتشده که توسط محیط الاستیک احاطهشده و تحت فشار خارجی قرار دارد، ارائه شده است. محیط الاستیک بر حسب دو پارامتر بستر الاستیک مدل پیشنهادی وینکلر- پاسترناک فرض شده است. جنس تقویتکنندهها نیز مدرج تابعی میباشد. روابط کرنش-جابهجایی با توجه به روابط غیرخطی فنکارمن و تئوری کلاسیک پوستهها بهدست آمده است. برای حل دینامیکی غیرخطی مسأله از روش تقویتکنندههای تکهای و روش گالرکین استفاده شده است. با در نظر گرفتن یک عبارت سه جملهای برای شکل خیز، رابطه فرکانس-دامنه ارتعاش غیرخطی به فرم سادهای تبدیل میشود. پاسخ دینامیکی غیرخطی با روش رانگ کوتا مرتبه چهارم به دست میآید. رفتار کمانش دینامیکی غیرخطی پوستههای مدرج تابعی تقویتشده نیز بر اساس معیار بدیانسکی- راث بررسی میشود. اثر پارامترهایی از جمله تقویتکنندهها، بستر الاستیک و نیروی محرکه بر منحنی ارتعاش غیر خطی فرکانس- دامنه و تأثیر میرایی و سرعت بارگذاری بر پاسخهای دینامیکی غیر خطی پوستههای استوانهای مدرج تابعی، بررسی شده است. همچنین فرکانسهای طبیعی، بارهای کمانش استاتیکی و دینامیکی غیرخطی نیز محاسبه شده است.
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