Stability Analysis and Vibration Reduction for A Two-dimensional Nonlinear System

This study examines how the vibration absorbers influence the stability of nonlinear flow-solid interaction systems. A novel approach is proposed for the analysis of dynamic stability of the two-dimensional nonlinear system using the internal resonance contour plot (IRCP) and flutter speed contour plot (FSCP). The system considered is a planar rigid-body with plunge and pitch vibrations. The two ends of the body are supported by cubic nonlinear springs with quadratic damping. The vibration absorber attached beneath is also considered as a rigid body, with the mass and position of the absorber adjusted for optimization of vibration reduction. The method of multiple scales (MOMS) is employed to obtain a fixed point solution. The P-method is also adopted to obtain the eigen plot and Poincaré Map for comparison. Finally, both the IRCP with FSCP are cross-referenced to provide guide-lines for identifying the optimal location for the absorber with regard to stability and vibration reduction without the need to alter the framework of the main body.