تحلیل اثر لقی بر ناپایداری بالواره دو درجه آزادی در جریان تراکم‌ناپذیر زیر صوت

نوع مقاله: مقاله پژوهشی

نویسندگان

1 عضو هیات علمی / دانشکده مهندسی هوافضا، دانشگاه صنعتی خواجه نصیرالدین طوسی

2 کارشناس ارشد / دانشکده مهندسی هوافضا، دانشگاه صنعتی خواجه نصیرالدین طوسی

چکیده

در این مطالعه از قابلیت تحلیل ارتعاشات اتفاقی برای یک سیستم آیروالاستیک غیرخطی استفاده می‌شود تا بتوان ناپایداری این سیستم غیرخطی را بدون ورود به حوزه زمان و استفاده از روش‌های عددی مرسوم و همچنین بدون بررسی نوسانات چرخه حد بررسی کرد. برای این منظور از یک بالواره دو درجه آزادی با عامل غیرخطی لقی تحت جریان شبه‌پایا استفاده می‌شود. در ابتدا فرض می‌گردد که علاوه بر نیروی برآ و ممان آیرودینامیکی یک نیروی اتفاقی به صورت نویز سفید و با تابع چگالی احتمال گوسین به بالواره غیرخطی وارد می‌گردد. با استفاده از روش خطی سازی آماری و آنالیز ارتعاشات اتفاقی سیستم‌های غیرخطی، معادله یک نگاشت غیرخطی یک بعدی برای واریانس پاسخ و سرعت جریان به دست می‌آید. از تحلیل این نگاشت یک معادله جبری غیرخطی شامل دو متغیر واریانس پاسخ و سرعت جریان ایجاد می‌گردد، و با حل این معادله برای سرعت‌های مختلف جریان، سرعت ناپایداری سیستم غیرخطی در نقطه واریانس بیشینه محاسبه می‌شود. در نهایت با تحلیل این معادله غیرخطی پدیده پرش در نمودار سرعت- واریانس در  نقطه دوشاخگی مماسی بررسی می‌گردد.

کلیدواژه‌ها


عنوان مقاله [English]

Analysis of Effect of Freeplay on Flutter of an Airfoil in Incompressible Subsonic Flow

نویسندگان [English]

  • Saeed Irani 1
  • Saeed Sazesh 2
چکیده [English]

In this study the compatibility of nonlinear random vibration analysis is used and extended to the nonlinear aeroelastic systems to investigate the instability of these systems with using neither time domain analysis nor limit cycle oscillations. To this aim a 2-degree of freedom airfoil with freeplay nonlinearity under quasi steady flow is used. At first one random Gaussian white noise is added to the aerodynamic lift force then the statistical linearization and the random vibration analysis of the nonlinear systems are used to obtain a nonlinear map of variance of the response with flow velocity as the control parameter. This nonlinear map leads to a nonlinear algebraic equation which consists of two parameters as the flow velocity and variance of the response. Solving this nonlinear equation for various flow velocities, ultimate to calculate the flutter speed where maximum of variance of the response happens. Finally the jump phenomenon is investigated where tangent bifurcation point occurs.

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