نویسندگان
دانشکده مهندسی مکانیک، دانشگاه تبریز، تبریز
چکیده
در این پژوهش، تعاملات مودال غیرخطی ناشی از تشدید داخلی یک به سه در سیستم تیر- جرم- فنر- میراگر بر اساس روش شناسایی سیستم غیرخطی مورد بررسی قرار گرفته است. بدین منظور معادلات حاکم بر ارتعاش عرضی تیر و جرم متمرکز بر اساس روش مقیاس‌های چندگانه مورد تحلیل قرار گرفته و پاسخ ارتعاشات سیستم تحت تشدید اصلی استخراج شده است. سپس رفتار فرکانسی پاسخ ارتعاشی با استفاده از تبدیل‌های فوریه و موجک مورلت بررسی شده است. به‌منظور شناسایی غیرپارامتریک پاسخ زمانی، توابع مود ذاتی تک فرکانسی با استفاده از روش تجزیه مود تجربی پیشرفته به‌دست آمده است. در این روش برای جلوگیری از اختلاط مود ناشی از تعامل مودال از سیگنال‌های پوششی استفاده شده است. پس از تحلیل رفتار فرکانسی هر یک از توابع مود، دینامیک جریان آهسته سیستم تشکیل شده و نوسانگرهای مودال اصلی برای بازسازی مود ذاتی متناظر استخراج شده است. درنهایت با تحلیل پدیده ضربان در یک سیستم یک درجه آزادی ساده نشان داده شده است که تشدید داخلی تنها در شرایطی باعث به‌وجود آمدن پدیده ضربان در پاسخ زمانی می‌شود که شیب دامنه لگاریتمی نیروی نوسان‌گر غیرصفر باشد. نتایج نشان می‌دهد که بر اساس متناوب، شبه متناوب و آشفته بودن پاسخ، تعاملات مودال می‌تواند پایا یا ناپایا باشد. همچنین رفتار آشوبناک بیشتر در مود ارتعاشی رخ می‌دهد که توسط مکانیزم تشدید داخلی تحریک شده است.
کلیدواژه‌ها
عنوان مقاله [English]
Identification of Nonlinear Modal Interactions in a Beam-Mass-Spring-Damper System based on Mono-Frequency Vibration Response
نویسندگان [English]
- M. H. Sadeghi
- S. Lotfan
چکیده [English]
In this paper, nonlinear modal interactions caused by one-to-three internal resonance in a beam-mass-spring-damper system are investigated based on nonlinear system identification. For this purpose, the equations governing the transverse vibrations of the beam and mass are analyzed via the multiple scale method and the vibration response of the system under primary resonance is extracted. Then, the frequency behavior of the vibration response is studied by Fourier and Morlet wavelet transforms. In order to perform the nonparametric identification of the time response, mono-frequency intrinsic mode functions are derived by the advanced empirical mode decomposition. In this approach, masking signals are utilized in order to avoid mode mixing caused by modal interaction. After analyzing the frequency behavior of each mode function, slow flow dynamics of the system is established and intrinsic modal oscillators for reconstructing the corresponding intrinsic mode are extracted. Finally, by analyzing the beating phenomenon in a simple one-degree-of-freedom system, it is shown that the internal resonance causes beating only under the circumstance that the slope of the logarithmic amplitude of oscillator force is nonzero. The results, therefore, show that depending on the periodic, pseudo-periodic, and chaotic behavior of the response, modal interactions might be stationary or non-stationary. Moreover, the chaotic behavior occurs mostly in the vibration mode excited by the internal resonance mechanism
کلیدواژه‌ها [English]
- Beam-mass-spring-damper system
- Nonlinear modal interactions
- Nonlinear system identification
- Advanced empirical mode decomposition
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