Effect of Dynamic Vibration Absorber on Fixed-free 3D Nonlinear Beam Embedded in Elastic Foundation

• Main Authors: Shu-Chien Tu, 塗舒茜
• Other Authors: Yi-Ren Wang 王怡仁
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/00046122032054958533

碩士 === 淡江大學 === 航空太空工程學系碩士班 === 103 === Vibration has long played a crucial role in engineering due to its effects on structural stability, metal fatigue, and structural damage to materials. Beams are used in a wide range of engineering problems and the internal resonance of nonlinear beam vibrations is a popular research topic. Internal resonance is unique to nonlinear systems in which integer relationships exist among the natural frequencies with various modes. This study examined the vibrations of a 3D fixed-free nonlinear beam placed on a nonlinear elastic foundation. We found that specific combinations of elastic modulus in the elastic foundation resulted in 1:3 internal resonances in the 1st and 2nd modes of the beam. This prompted us to add a Tuned mass damper (TMD) on the elastic beam in order to prevent internal resonance and suppress vibrations. We analyzed this nonlinear system using the method of multiple scales (MOMS). Fixed points plots were also used to facilitate the observation of internal resonance. This made it possible for us to study the influence of nonlinear geometry and nonlinear inertia associated with the vibration of the elastic beam. In this work, we examined the combination of optimal mass ratio and elastic modulus as well as the location of the TMD in order to prevent internal resonance and achieve optimal damping effects. Finally, the numerical results were compared with the fixed points frequency plots to confirm the findings from this study.