کنترل ارتعاشات عرضی تیر تحت تحریک هارمونیک خارجی توسط چاه‌غیرخطی انرژی

نوع مقاله: مقاله مکانیک

نویسندگان

1 باشگاه پژوهشگران جوان و نخبگان، واحد تهران جنوب، دانشگاه آزاد اسلامی، تهران، ایران

2 باشگله پژوهشگران جوان و نخبگان، واحد تهران جنوب، دانشگاه آزاد اسلامی، تهران، ایران

چکیده

در این مقاله به بررسی رفتار ارتعاشی یک تیر دوسرگیردار متصل به یک جاذب غیرخطی ارتعاشاتی که تحت بار نوسانی با دامنه‌های تحریک مختلف است، پرداخته شده است. این سیستم در واقع یک مدل ساده و محلی از سازه‌های دریایی تحت تحریک سیال خارجی را ارائه می‌دهد. برای مدل-سازی تیر از تئوری اویلر-برنولی و برای مدل‌سازی جاذب (چاه غیرخطی انرژی)، از فنر غیرخطی و دمپر خطی استفاده شده است. پاسخ سیستم به صورت تحلیلی (روش متوسط‌گیری مختلط شونده) و عددی (روش رانگ-کوتای مرتبه چهارم)، به دست آمده است و بر این‏ اساس محدوده مناسب پارامترهای جاذب، برای کاهش بهینه ارتعاشات استخراج شده است. علاوه بر این شرایط رخداد انشعابات زین اسبی و هاپ عام و همچنین تأثیر آن‌ها در رخداد نوسانات تخفیفی در سیستم بررسی شده است. نتایج نشان دادند که میرایی چاه غیرخطی انرژی، تأثیر زیادی بر روی کارایی آن دارد. در ضمن با نزدیک شدن محل نصب جاذب به تکیه‌گاه‌ها احتمال رخداد پدیده نوسانات تخفیفی کاهش می‌یابد و پاسخ گذاری سیستم نیز طولانی‌تر می‌شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Lateral vibration control of a beam subjected to the harmonic external load using a nonlinear energy sink

نویسندگان [English]

  • Ali Ebrahimi Mamaghani 1
  • Hoda Sarparast 2
1 Young Researchers and Elite Club, South Tehran Branch
2 YoungResearchers and Elite Club, South Tehran Brancj, Islamic Azad university, Tehran, Iran
چکیده [English]

Annihilating of unwanted vibrations of mechanical systems is one of the necessary requirements of designers over years. This current paper investigates dynamical behavior of a clamped-clamped beam attached to a Nonlinear Energy Sink (NES) under the harmonic force with different amplitudes. The nonlinear absorber consists of a linear damper and an essentially nonlinear stiffness. The considered system is a simple model of offshore structures subjected to the external fluid flow. In order to simulate the primary system, Euler-Bernoulli beam theory has been applied. Occurrence of Strongly Modulated Responses (SMR) under sinusoidal load reflects the efficiency of the absorber. Analytical approach (complexification-averaging method) and numerical solution (Runge-Kutta method) are applied for comparison and validation of the results. The boundaries of occurrence of Saddle-node and Hopf bifurcations and relaxation oscillations are obtained. The results show that the NES damping has substantial influence on the NES performance. Furthermore, by approaching the NES location to the beam supports, the probability of occurrence of the SMR decreases and the transient responses of the system lasts longer.

کلیدواژه‌ها [English]

  • clamped-clamped beam
  • nonlinear energy sink
  • strongly modulated responses
  • relaxation oscillations
  • phase plane
 

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