Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 30, No. 10 (October 2017) 1545-1554    Article in Press

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  THE TRANSIENT DYNAMICS OF A BEAM MOUNTED ON SPRING SUPPORTS AND EQUIPPED WITH THE NONLINEAR ENERGY SINK
 
S. Mahmoudkhani
 
( Received: May 12, 2017 – Accepted in Revised Form: July 07, 2017 )
 
 

Abstract    The transient dynamics of a beam mounted on springer-damper support and equipped with a nonlinear energy sink (NES) is investigated under the effects of shock loads. The equations of motion are derived using the Hamilton’s principle leading to four hybrid ordinary and partial differential equations and descritized using the Galerkin method. An adaptive Newmark method is employed for accurate and efficient numerical simulation and the results are used to assess the efficiency of the NES by conducting various parametric studies. The mechanisms of targeted energy transfer from the beam to the NES are indicated using the wavelet transform and Hilbert–Huang transform of the responses. Numerous modes are recognized to contribute to the response and the modes with smaller particiaption of the rigid-body motions are found to be strongly engaged in the transient resonance capture (TRC) at the initial stage of the motion. The modes with dominant rigid-body motions are, however found to be less engaed in an effective TRC. The enhanced empirical mode decomposition, with different masking signals are used to extract narrow-band intrinsic mode functions (IMFs) and simultaneous 1:1 transient resonances are observed between different IMFs of the responses especially at the initial stage of the motion.

 

Keywords    Nonlinear energy sink, Transient dynamics, Nonlinear resonance interaction, Targeted energy transfer, Empirical Mode Decomposition

 

چکیده    دینامیک گذرای تیر با تکیه­گاه­های فنری و مجهز به جاذب غیرخطی ارتعاش، تحت اثر بار شوک اعمالی مورد بررسی قرار گرفت. معادلات حاکم با استفاده از اصل همیلتون استخراج شد که منجر به چهار معادله دیفرانسیلی شامل معادلات معمولی و جزئی مربوط به مود­های صلب تیر، حرکت جاذب غیرخطی و و تغییرشکل الاستیک تیر شد. روش گالرکین نیز برای گسسته­سازی معادلات و دستیابی به معادلات زمانی مورد استفاده قرارگرفت. برای حل عددی از روش حل نیومارک با امکان تنظیم اتوماتیک گام­ استفاده شده و برای بررسی کارایی جاذب از طریق مطالعه پارامتریک به­کارگرفته شد. چگونگی انتقال هدفمند انرژی از تیر به جاذب نیز با استفاده از اعمال تبدیل ویولت و تبدیل هیلبرت-هوانگ به پاسخ زمانی مورد مطالعه قرار گرفت. مطالعات نشان دهنده حضور مودهای متعدد در پاسخ و درگیر شدن قابل توجه مودهای با سهم پایین از حرکت صلب تیر در پدیده تشدید گذرا در زمان­های ابتدایی حرکت بود که منجر به میرایی قابل توجه انرژی در تیر می­شد. در مقابل، مودهای با سهم بیشتر از حرکت صلب به میزان کمتری درگیر با تشدید گذرا شدند. از روش تجزیه مود تجربی در کنار سیگنالهای ماسک مختلف نیز برای استخراج توابع مود ذاتی استفاده شده، و تشدید 1:1 بین مودهای ذاتی حاضر در پاسخ، به­ویژه در زمان­های ابتدایی مشاهده شد.

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