The Study of A Nonlinear Suspension Elastic Beam with An End Point Dynamic Vibration Absorber

• Main Authors: Chia-Man Chang, 張家嫚
• Other Authors: 王怡仁
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/71955259940263791315

碩士 === 淡江大學 === 航空太空工程學系碩士班 === 101 === This study investigated the performance of a mass-spring dynamic vibration absorber (DVA) at the free end of a hinged-free elastic beam under simple harmonic excitation. This beam system was suspended by suspension cables. These cables were simulated by cubic nonlinear springs to examine the nonlinear characteristics of this system. The combination of mass and spring constant of the tip-attached dynamic vibration absorber (DVA) were investigated. This time-dependent non-homogeneous boundary condition problem was solved by Mindlin-Goodman method. By using the shifting polynomial function, one can transform this system to a homogeneous boundary problem. The method of multiple scales (MOMS) was performed to solve the nonlinear equations. The 1:3 internal resonance was found at the 1st and 2nd modes of this beam system. The fixed point plots were obtained and compared with the numerical results to verify the system internal resonance. The Poincare Map was also utilized to identify the system instability frequency region of the jump phenomenon. The parameters of the tip attached DVA were studied. The internal resonance can be avoid for the existence of the DVA. The optimal DVA mass and the spring constant were provided for best beam vibration reduction. Finally, the wind speeds and aerodynamic loads were included to investigate the stability of this system. The system stability was analyzed by Floquet theory and Floquet multipliers. The basin of attraction charts were made to verify the effects of the combinations of DVA’s mass and the spring constant at diverge speed.