Abstract    Abstract In vibratory systems, linear and nonlinear vibration absorbers can be used to suppress the primary and super-harmonic resonance responses. In this paper, the behavior of a nonlinear system with a nonlinear absorber, under the primary and super-harmonic resonances is investigated. The stiffnesses of the main system and the absorber are cubically nonlinear and the dampers are linear. Multiple time scales method is used to obtain approximate solution of the nonlinear equations of motion. Results show that at primary resonance, a linear absorber can suppress the peak amplitude of the system better than a non-linear one. But under super-harmonic resonance, the vibration amplitude can be more effectively reduced by adding a nonlinear absorber to the vibrating system.

Keywords    Nonlinear vibrations, Primary resonance, Super-harmonic resonance, Non-linear absorber, Multiple time scales.

چکیده    چکیده در سیستم­های ارتعاشی، به منظور جلوگیری از تشدیدهای اولیه و سوپرهارمونیک، می­توان ازجاذب­های دینامیکی خطی یا غیرخطی استفاده کرد. در این مقاله، رفتار یک سیستم غیرخطی به همراه یک جاذب غیرخطی، تحت تشدیدهای اولیه و سوپرهارمونیک، مورد بررسی قرار می­گیرد. سختی سیستم اصلی و جاذب غیرخطی از نوع درجه­ی سه می­باشد و میراکننده­ها خطی هستند. برای به دست آوردن حل تقریبی معالات غیرخطی حرکت، از روش مقیاس زمانی متعدد­استفاده شده است. نتایج نشان می­دهند که در تشدید اولیه در جلوگیری از ماکزیمم دامنه­ی سیستم، یک جاذب خطی عملکرد بهتری نسبت به جاذب غیرخطی دارد. اما تحت تشدید سوپرهارمونیک، با اضافه کردن یک جاذب غیرخطی به سیستم ارتعاشی ، دامنه­ی ارتعاش بیشتر از وقتی جاذب خطی است، کاهش می­یابد.

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