Analysis Of Vibration Characteristics And Response Of Post-buckling Panel Structure

Aircraft used a large number of thin shell structure to reduce the weight.But these thin shell structures will bear various loads with the faster flight speed,including thermal load generated by friction and strong noise load caused by the thrust.Thermal expansion will cause buckling of thin-walled structures under the thermal load and the effect of noise load may cause these thermal buckling thin-walled structures to undergo the jump on the buckling configuration.A detailed research of structural characteristic after buckling,vibration characteristics around the buckling,and mechanism of the jumping,has important significance to fully tap the post buckling bearing capacity,optimize the structure,and improve the reliability of structure.This paper is based on the Von-Karman theory of generalized large deflection,considering the geometric nonlinearity,deducting the nonlinear dynamic equation of thin wall in the common effect of thermal load and lateral load of structure,and analyzing the problems of thin plate vibration from two ways.The first way regards the vibration of thin plate after buckling as small linear vibration around the post-buckling equilibrium position,divides the transverse displacement of thin plate into buckling displacement and small vibration displacement,and uses the Galerkin method to solve the problem.First,the variation of critical buckling temperature and buckling amplitude of each simply supported and clamped quadrilateral thin plate with temperature are obtained regarding the presence of a temperature gradient.The results show that the plate has many equilibrium configurations after buckling,the increase of temperature will increase the buckling deformation,and the existence of temperature gradient will influence the post-buckling path of the plate's partial configuration.Then,the change of the linear frequency with the temperature after buckling is calculated according to the buckling amplitude,and the influence of the buckling configuration on the vibration frequency of the thin plate after buckling is discussed.Finally,the modal superposition method is used to obtain the vibration response of the plate under lateral load excitation.The second way is to deduce the nonlinear vibration equation of thin plate under the action of uniform heat load and transverse load by means of Galerkin method.We can obtain the nonlinear response of thin plate by the numerical solution,analyze the nonlinear free vibration of heated thin plate and the response of harmonic excitation under the forced response and noise,and discuss the jump phenomena of thin plate.The analysis on the free vibration response of plate show that plate will jump when the input energy to post buckling plate is enough,and changes in nonlinear vibration frequency around the jump with different vibration amplitude are different.Through the forced vibration analysis under harmonic excitation,it is found that when the frequency of the exciting force approaches the natural frequency of the plate,the plate will resonate,the amplitude will increase sharply,and even the springboard will occur.In addition to the numerical solution,we also give the exact probability density solution according to the Fokker Planck equation in the response analysis of the thin plate subjected to noise.So we can use the potential well depth to represent the degree of difficulty of sheet jump in noise loads.It is found that the deeper the potential well depth is,the more difficult it is to occur.Through the parameter analysis,the effects of the excitation intensity,damping,stiffness and temperature change on the random jump response are given.The high value of thermal load and stiffness of plate will inhibiting jump,but high heat load will cause large deformation buckling,so it is key to find a balance between the suppression of jump and the low buckling deformation by changing the nonlinear the stiffness of the structure.