本研究以一非線性彈性樑為主體模型，其兩端皆以鉸接(Hinge)支撐，並且以非線性彈簧來懸吊或支撐之。此懸吊系統可用來模擬一般吊橋之振動；若將非線性彈簧倒置改以支撐的方式，亦可模擬此彈性樑置放於任何的彈性基座(Elastic Foundation)。此系統可以被應用在橋墩橋樑工程、捷運軌道、輸油管及海底電纜等，因此本研究極具應用價值。在本研究中，吾人分別於此彈性樑的不同位置加載不同質量之Lump-Massed Dynamic Vibration Absorber (LM-DVA)，而此質點之下方另以一彈簧支撐之。本研究欲分析，在以非線性彈簧支撐或懸吊之彈性樑的振動情況下，LM-DVA的擺放位置、質量大小與彈簧之彈性係數對於整體振動的影響。本研究利用各模態(mode)之頻率響應(Frequency Response)，將系統之最大振幅以3D Maximum Amplitude Contour Plot (3D MACP)表示，觀察出此LM-DVA的最佳組合，達到本系統之最佳減振效果，以獲得最終結論。 The issue of vibration has always been a concern for researchers and engineers and vibration within nonlinear systems is particularly problematic. Beams, the subject of this study, are essential elements of engineering structures with a wide range of applications. This study considered a slender hinged-hinged nonlinear elastic beam with suspension cables simulated using nonlinear cubic springs and linear dampers to allow greater amplitude in the transverse direction. The model in this study could be applied to the engineering of structures with nonlinear suspension systems. In addition, inverting the system, we could simulate the beam placing on a Winkler-type elastic foundation. Therefore, there is a wide range of applications for this system. The primary objective of this study was to add a point mass on the beam to formulate a Lump-Massed Dynamic Vibration Absorber (LM-DVA) system to avoid internal resonance within this beam and achieve effective vibration damping. The lumped mass on the beam could change the boundary conditions of the beam system and separate this nonlinear beam into two parts. The influence of stretching effect and the location of the lumped mass were also taken into account. We employed the method of multiple scales (MOMS) to analyze this nonlinear problem. The Fixed point plots (steady state frequency response) were obtained. LM-DVA with various locations and spring constants were considered and the optimal mass range for the LM-DVA to reduce vibration in the main structure was also proposed by using the novel concept of 3-dimensional maximum amplitude contour plots (3D-MACP). The results of this study were verified using numerical simulation, which, in addition to confirming the accuracy by through comparison, established the applicability in this study.
