Nonlinear Vibration Analysis of an Euler-Bernoulli Beam Resting on a Nonlinear Elastic Foundation under Compressive Axial Force
الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکاحمد مامندی 1 , محمدحسین کارگرنوین 2
1 - استادیار، دکترای مهندسی هوافضا، دانشکده مهندسی مکانیک، واحد پرند، دانشگاه آزاد اسلامی، تهران، ایران
2 - استاد، دانشکده مهندسی مکانیک، دانشگاه صنعتی شریف، تهران، ایران
الکلمات المفتاحية: Euler-Bernoulli beam, Nonlinear vibrations, Nonlinear elastic foundation, The 3:1,
ملخص المقالة :
This paper studies the nonlinear vibration analysis of a simply supported Euler-Bernoulli beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes concept in the case of three-to-one (3:1) internal resonance. The beam’s governing nonlinear PDE of motion and also its boundary conditions are derived and then solved using the method of Multiple Time Scales. Under three to-one-internal resonance condition applying nonlinear normal modes the steady state stability analysis of the beam’s vibrations is performed. Then the effect of changing the value of different parameters on the beam’s dynamic response and the steady state stability analysis is investigated.
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