نویسندگان
دانشکده مهندسی مکانیک، دانشگاه صنعتی شاهرود، شاهرود
چکیده
رفتارهای پیچیده غیرخطی مانند حرکت آشوبناک، اثرات نامطلوب و مخربی بر سیستم‌های دینامیکی دارند. در این تحقیق رفتار غیرخطی ورق ویسکوالاستیک مستطیلی با لبه‌های مفصلی، تحت اثر جریان آیرودینامیکی مافوق صوت مورد بررسی و تحلیل قرار گرفته و نتایج با ورق الاستیک غیرخطی مقایسه شده است. معادلات ورق با استفاده از تئوری ورق کلاسیک به‌دست آمده و از روابط کرنش- جابه‌جایی ون- کارمن نیز به‌منظورملاحظه اثرات غیرخطی هندسی استفاده شده است. مدل کلوین ویت برای توصیف خاصیت ویسکوالاستیک و "تئوری شبه پایای پیستون مرتبه اول" نیز به‌منظور مدل‌سازی جریان آیرودینامیکی مافوق صوت به‌کار گرفته شدند. معادلات حرکت ورق از روش لاگرانژ استخراج و سپس با روش رایلی- ریتز گسسته‌سازی شد. معادلات با استفاده از روش رانگ کوتای مرتبه چهار حل و برای بررسی رفتار دینامیکی ورق، مقادیر ویژه سیستم و نیز نمودارهای پاسخ زمانی، فضای فازی، نگاشت پوانکاره، طیف توانی و نمودار چندشاخگی مورد مطالعه و تحلیل قرار گرفت. نتایج نشان می‌دهد که در برخی نسبت‌های منظری، آستانه وقوع فلاتر در ورق ویسکوالاستیک پایین‌تر از ورق الاستیک است. از سوی دیگر با افزایش پارامتر کنترلی، به‌جای رفتارهای پیچیده غیرخطی مانند آشوب در ورق الاستیک، در ورق ویسکوالاستیک رفتارهای ساده‌تری نظیر حرکت پریودیک رخ می‌دهد.
کلیدواژه‌ها
عنوان مقاله [English]
Analysis and Comparison of Nonlinear Dynamic Behavior of Viscoelastic and Elastic Rectangular Plates under Supersonic Aerodynamic Flow
نویسندگان [English]
- H. Asadigorji
- A. Karami mohammadi
چکیده [English]
Complex nonlinear behaviors such as chaotic motion have devastating effects on dynamic systems. In this study, nonlinear behavior of simply supported rectangular viscoelastic plates was examined during supersonic aerodynamics and compared with the nonlinear elastic plate. Classical plate theory was used to obtain the plate equations, and Von- Kármán strain-displacement relations were used to consider the nonlinear geometric effects. The Kelvin Voigt model was also used to describe the viscoelastic properties and the “first-order piston theory" was used for supersonic aerodynamic flow. The equations of motion of the rectangular plate were extracted using the Lagrangian method and then, discretized by the Rayleigh-Ritz method. Solution of the equations was performed using fourth order Runge Kutta method. To investigate the dynamic behavior of the plates, the eigenvalues of the system, time history curves, phase portraits, Poincaré maps, and bifurcation diagrams were studied and analyzed. The results show that in some aspect ratios, the threshold for the occurrence of the flutter in the viscoelastic plate will be lower than that in the elastic plate. On the other hand, when the control parameter increases, complex nonlinear behavior such as chaos in the elastic plate goes simpler in the viscoelastic plate, such as periodic motion.
کلیدواژه‌ها [English]
- Rectangular Viscoelastic Plate
- Supersonic Aerodynamic Flow
- nonlinear dynamics
- Bifurcation Diagrams
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