بررسي پايداري و رفتارهاي ديناميكي غيرخطي لوله‌ي حامل سيال در حالت سه‌بعدي

Three-dimensional flutter and nonlinear dynamical behavior analysis of fluid conveying pipes

در اين مقاله به مدل‌سازي و بررسي فلاتر (اهتزاز) و رفتارهاي غيرخطي در لوله‌ي حامل سيال در حالت سه‌بعدي پرداخته خواهد شد. معادلات حاكم بر سيستم، با فرض يك ميدان جابه‌جايي مناسب به‌صورت غيرخطي و با استفاده از اصل لاگرانژ استخراج شده است. اين امر نياز به مدل‌سازي پيچيده را، با توجه به مطالب ذكر شده در مطالعات پيشين، از بين مي‌برد. با توجه به حركت سه‌بعدي لوله، جابه‌جايي ها به‌صورت دو خمش و يك حركت درون‌صفحه‌يي مدل‌سازي شده‌اند. معادلات ديفرانسيل مشتقات جزيي حاكم با استفاده از روش رايلي ـ ريتز به معادلات ديفرانسيل معمولي تبديل‌، و با استفاده از پارامترهاي مناسب بي بعد‌سازي شده است. سپس معادلات غيرخطي به روش عددي حل شده و رفتار هاي ارتعاشي آن مورد بررسي قرار گرفته است. نتايج به‌ دست ‌آمده، و مقايسه‌ي آن با نتايج ارايه شده در منابع، حاكي از دقت روش مدل‌سازي ارايه‌شده با توجه به ميدان جابه‌جايي مفروض است.

In this work, the modeling and flutter and nonlinear dynamical behaviors of fluid-conveying pipes in three dimensions are undertaken. All equations of motion are derived assuming an appropriate displacement in nonlinear form using Lagrange principle to circumvent the complex modeling approach given in mentioned references. In previous works on modeling three-dimensional motion of pipe, a complex approach based on inextensibility of pipe was used for derivation of equation of motion. This assumption resulted in nonlinear complex equation of motion and boundary condition. But, here, a simple method is used to obtain equation of motion. Due to three-dimensional motions of pipe, double bending and in-plane displacement field are assumed. Governing partial differential equations are discretized by Rayleigh–Ritz’s method, and dimensionless form of equation is derived with defining appropriate parameters. The nonlinear equations are solved numerically and its vibration behavior is examined. Due to fluid flow, detrimental flutter phenomenon occurs, which make system unstable. Different types of bifurcations are observed, and the effect of varying parameters on flutter is accurately examined. Discussion of how flutter occurs and different modes of flutter are presented. Finally, the effect of design parameters on the system instability and its type is presented. With varying flow velocity, different types of nonlinear vibrations are occurred. These behaviors include simple limit cycle oscillations, period doubling, intermittency, and chaos. Also, in some flow velocities, locking motion in a special plane is occurred. The effects of different parameters on these nonlinear behaviors are examined. Some new results are presented, which are not previously reported. Obtained results and their comparison with appropriate references show the accuracy of modeling according to the assumed field displacement. Obtained results show the efficacy of the proposed modeling in capturing all nonlinear behavior phenomenon reported in literature. It is simple to extend the proposed modeling for different boundary conditions.