Research Of Experimental Modeling For Multi-degree-of-freedom System Under Parametric Excitation

Most of the vibration in the fields of aerospace, machinary and shipbuilding are high-demensional vibration,including periodic,quasi-periodic and chaotic system.Considering the reality and complexity of above engineering,theory modeling may lead to obvious deviation between the equation and the actual system beacause of approximation and simplification.This paper aims to establish the dynamic equation of experiment system with the experimental modeling method,which is made up of experimental data and identification theory.Incremental harmonic balance nonlinearity identification method has already been applied to the experimental modeling method for single-degree-of-freedom dynamical equation and shows reasonable match between numerical simulation and experimental system. This paper aims to apply the IHBNID to multi-degree-of-freedom nonlinear parametric and forced excitation vibration system. So the experimental platform of L-shape beam system is set up and the dynamical equation of the beam is built with the experimental modeling method and the IHBNID. The result of numerical simulation shows fairly good compatibility with experimental system on qualitative and quantitative aspects. This theory including experimental modeling method and the IHBNID demonstrates that it also can be applied to experimental systems with variable frequencies and motions, such as the period-doubling motion.The IHBNID method is suitable for the periodic response and is applied to the quasi-periodic response that the Fourier series frequencies are irreducible.The power spectrum analysis and the Poincare mapping based on the numerical simulation for a two-freedom nonlinear system demonstrate that the response is quasi-periodic vibration.The parameters is identified with the IHBNID method for quasi-periodic response and the deviation is analysed.