Identification Of The Nonlinear Vibration Characteristics Of Reinforced Concrete Beams Based On Wiener Kernel

There are a lot of nonlinear factors in civil engineering, such as materialnonlinearity resulted from Stress- strain constitutive relationship, Geometry nonlinearresulted from large elastic deformation and boundary nonlinearity resulted from thechange of constraint boundary conditions. Reinforced concrete beams are importantstructure components of civil engineering and present a certain non-linearcharacteristics during vibration for their materials obvious non-linearity. When thebeams have crack for damage, the stiffness of beams will degrade, the damping willchange, and the crack will open and close when vibrate, all this conditions willstrength the characteristic of nonlinear vibration. Furthermore, the nonlinearity of thereinforced concrete structure increases with the damage of the structure. So thevibration system is mostly nonlinear system in practical engineering. In recent years,the rapid development of computer technology has promoted the research andapplication of nonlinear system theory greatly.Volterra functional series and Wiener functional series are two kinds of theimportant functional series describing nonlinear system. The general frequencyresponse functions (MFRF) of nonlinear system have specific physical meaning, theydescribe nonlinear system directly. In order to avoid the dimension disaster ofVolterra series in practical application, several terms of Volterra frequency kernelwere adopted to simulate the nonlinear system. However, the terms of Volterra seriesare not orthogonal, nonlinear system whose nonlinear characteristics are unknown orthey can not be described by analytic expression can not be described by Volterraseries. It was found that Wiener kernels can describe this kind of nonlinear system.The role of Wiener kernels of nonlinear system is the same as the impulse response oflinear system and they can describe nonlinear system completely. If an input signal isthe Gaussian white noise, the Wiener kernels can be estimated through calculating thecross-correlation functions of the input and output of a nonlinear system.In chapter 1 and chapter 2 of this paper, firstly, the author introduced the state ofresearch on nonlinear vibration and damage identifying at home and abroad. Secondly,the author introduced two kind of nonlinear models. Lastly, the author expounded thenonlinear vibration of reinforced concrete beams for material nonlinearity, geometrynonlinearity and cracks. In chapter 3, identification of the nonlinear vibration characteristics based on theWiener kernels was studied. If an input signal is the Gaussian white noise, the Wienerkernels can be estimated through calculating the cross-correlation functions of theinput and output of a nonlinear system. The numerical examples show that Wienerkernels can reflect the strength of polynomial nonlinear system well. The high orderWiener kernels of linear system are close to 0 and the second order Wiener kernel ofquadratic nonlinear system is obvious not close to 0 . For cube nonlinear system, thesecond order Wiener kernel is close to 0 while the cube Wiener kernel is obvious notclose to 0. The value of variance of cube Wiener kernel shows the strength ofnonlinearity well just for cube nonlinear system.Muti-dimension Frequency Response Function (MFRF) is key when nonlineardynamic system is analysis by Volterra series model in frequency domain. In fact, wecan get MFRF by the MFRF of skeleton linear system. So the research on skeletonlinear system is absolute important. In chapter 4, firstly, the definition of skeletonlinear system was representing. Secondly, it was proved that the MFRF of polynomialnonlinear system can be expressed by the MFRF of skeleton linear system completely.Lastly, the calculation method was representing. It was show that the MFRF ofskeleton linear system neglect effect of nonlinearity and it has nothing to theexcitation magnitude. If the nonlinear system was analysis by linear theory, thefrequency is related to the excitation magnitude. So we can obtain the conclusion thatthe frequencies have changed though the character of structure has no change, and thedamage condition of structure was misjudged. The identification method of skeletonlinear system based on nonlinear vibration is more reasonable.Reinforced concrete beams are important structure components of civilengineering and present a certain non-linear characteristics during vibration for theirmaterials obvious non-linearity. Furthermore, the nonlinearity of the reinforcedconcrete structure increases with the damage of the structure. The research of thispaper provides foundation for damage identification of structure base on nonlinearvibration.