Research Of The Experimental Modeling For Viscoelastic Composite Beam Under Parametric Excitation

This thesis mainly studied the nonlinear mechanical behavior of nano-composited beams which were synthesized in the laboratory. It was difficult to establish the dynamical equation without basic mechanical parameters and constitutive relations. By Incremental Harmonic Balance Nonlinearity Identification (IHBNID) method and parametrically excited dynamic responses, the dynamical equation of the viscoelastic composite beam was established. Then this process was extend to multi-degree-of-freedom system which has periodic responses. At the same time, the dynamic mechanical properties of nano-composited beams were studied by experimental method. The coefficients of models used by now were optimized through genetic algorithm.Firstly, by taking the experimental modeling method and applying to the IHBNID method, the dynamical equation of the viscoelastic composite beam was then built. A series of discussions on the reasonableness of nonlinear term were showed. And different excited frequencies and different materials were considered. Based on numerical simulation, comparisons between theoretical model and experimental system show good agreement in qualitative and quantitative analysis. The theoretical model is applicable for a class of composite materials with different ratio of rutile nanoscaled titania. Frequency scanning data were used for system parametric identification with the dynamical equation. And then the relationships between frequency and parameters and relationships between material and parameters were discussed.Secondly, the IHBNID method excels in the computation accuracy and noise resistance for the single degree of freedom system. So IHBNID method was then extend to multi-degree-of-freedom systems with periodic responses. In order to test the accuracy of IHBNID in multi-degree-of-freedom systems, the method was used to identify the parameters of two degree Van der Pol-Duffing and Mathieu-Duffing equations. Compared with HBNID method, the effectiveness of IHBNID was verified and it applied to multi-degree-of-freedom systems well.Finally, the composite beams researched in this thesis were typical viscoelastic material. To make it easier for structural design and analysis, constitutive relation were developed. On the basis of predecessors'work, forced and non-resonance method was selected to test dynamic mechanical properties of the composite beams. And curve of storage modulus, loss modulus and loss factor as function of the frequency are gained experimentally. Then, an approach based on genetic algorithm is introduced to determine the parameters in a constitutive relation for viscoelastic materials according to the experimentally obtained material mechanical properties. The standard mechanical (STD), the ADF, and the GHM models are parametrically optimized. In addition, according to the optimal result of objective function, the advantages and drawbacks of each model are discussed. This work provides a solid foundation which allows for the analysis of complicated structures involving this damping material.