Nonlinear Dynamic Behavior Study Of Stiffened Plates Of Steel Box Girder

Facing the reality of the extensive use of orthotropic steel bridge deck in bridge structure,it is necessary to proceed a deep theoretical study for the nonlinear dynamic behavior of stiffened plate to find out the nonlinear vibration characteristics of the stiffening plate and sum up the relevant methods of vibration control.This article base on the structure characteristics of the stiffened plate of large span bridge steel box girder,through combining the method of theoretical derivation and numerical analysis,the nonlinear dynamic behavior of the stiffening plate has been studied systematically.Several aspects of the following work have been done:(1)Considering the influences of geometric nonlinearity,damping,initial geometric imperfection,the nonlinear vibration governing equation of the stiffened plate was deduced,the single-mode condition of weakly nonlinear free vibration and forced vibration of four edges simply supported stiffened plate and four edges clamped stiffened plate were studied.The analytical solution of the four edges simply supported and the four edges clamped stiffened plate under the weakly nonlinear free vibration and forced vibration were derived.For the weakly nonlinear free vibration of the stiffening plate,the quadratic analytical solution of single mode nonlinear dynamic differential equation were obtained by using the multiple scales method.The nonlinear characteristics of several vibration modal of the four edges simply supported and four edges clamped stiffened plate have been discussed through some numerical examples,which considering the influence of the initial geometric imperfection.For the weak nonlinear forced vibration of the stiffening plate,the quadratic approximation solution of primary resonance of single mode nonlinear dynamic differential equation were obtained by using the multiple scales method.The influences of the initial geometric imperfection to the amplitude-frequency relationship of main resonance were discussed through some numerical examples.(2)Considering the influences of geometric nonlinearity,damping,and initial geometric imperfection,the single-mode strongly nonlinear vibration of four edges simply supported and four edges clamped stiffened plate were studied.The analytical solution of four edges simply supported and four edges clamped stiffened plate under strongly nonlinear free vibration was deduced by using the Multiple Scales Lindstedt Poincare Method.The influences of the number of stiffener and the initial geometric imperfection were discussed by some numerical examples.Moreover,the applicability of the Multiple Scales Lindstedt Poincare Method,Modified Lindstedt Poincare Method and the Multiple Scales Method on the strongly nonlinear vibration analysis were discussed.(3)The nonlinear differential equation of parametric vibration of the stiffened plate with initial geometric imperfection was established.The nonlinear dynamic stability of the four edges simply supported and four edges clamped stiffened plate with initial geometric imperfection under in-plane cycle motivation were studied.Considering the different situation of the excitation parameters,the multiple scales method and incremental harmonic balance method have been used to solve the equation respectively.In the end,the influence of the number of stiffener,damping,initial geometric imperfection and the stiffener stiffness change on the dynamic unstable region of stiffened plate were discussed through some numerical examples.(4)The nonlinear thermal vibration of the stiffened plate under the effect of the temperature was studied.The nonlinear thermal vibration differential equation of stiffened plate was deduced by considering the uniform temperature field,the transverse temperature gradient,the geometric nonlinearity of stiffened plate,the eccentric stiffener and damping.Then,based on the nonlinear thermal vibration differential equation of the stiffened plate,the single-mode nonlinear thermal vibration of stiffened plate was studied,the influence of the uniform temperature field and the transverse temperature gradient on the nonlinear frequency of stiffened plate were discussed by some numerical examples.(5)The bifurcation phenomenon of nonlinear forced vibration of the stiffened plate was studied.The threshold of the external excitation amplitude at the bifurcation point of the vibration system was derived,and three kinds of bifurcation control method to eliminate the bifurcation phenomenon and reduce the amplitude of the vibration system like the adjustment of the number of the stiffener,stiffener stiffness and damping were discussed by numerical simulation,some conclusions which are benefic to the stiffened plate design were obtained.