Nonlinear Response With Buckling And Snap-through Of Stochastic Thermal-acoustically Excited Plates

In some kinds of machine,the thin composite plate which has heat resistant,light weight is used in the high temperature environment.The response of the thin plate suffering from the complex loading,such as mechanical loading,random sound-thermal loading,shows the nonlinear characteristics.Some researchers pay their attentions to nonlinear behaviors and stability of the thin plate at high temperature.In this thesis,we focus on the buckle and snap-through phenomenon of thin plate with initial imperfection and affected by some kinds of loadings,such as impact loads,harmonic loads,acoustic loads and random thermal loads.Firstly,using three fundamental equations of elasticity theory and the Kirch-hoff assumption,the nonlinear large defection equations of motion of the thin plate with initial imperfection are established based on the Von Karman theory.In the modelling,the thermal stress is considered,and internal stress is separated into two parts of uniform stress and one varying with position according to the fixed boundary condition.Then,the separation of variables is carried out by the Galerkin Process,and the effects of parameters,such as aspect ratio,numbers of mode used,initial imperfection,on critical buckling temperature of plate are investigated.The results show the critical buckling temperature increase when the aspect ratio of plate decrease,and the more numbers of mode are used,the higher the critical buckling temperature is.By addressing the simplified motion equation with one degree of freedom,the bending displacement of plate varies with buckling temperature and aspect ratio.Next,the ordinary differential equations with time-varying inertial terms and damping terms are calculated by the Runge-Kutta method.And the buckling and snap-through phenomena influenced by the temperature difference are analyzed.For no loading case,the buckling phenomenon emerges when the temperature difference is 50.4181 ?.The snap-through phenomena of the post-buckling plate suffering from impact load,harmonic load and random acoustic load are shown respectively.The Gauss-white noise acoustic load model with specified frequency and Sound Pressure Level(SPL)is set up and employed to analyze the vibration characteristic of the plate with different SPL load.Finally,the buckling and snap-though phenomena of plate under the random thermal loading obeying uniform distribution are shown.To obtain the random,continuous and smooth thermal load function,the cubic spline interpolation is used to interpolate the discrete data of random thermal load.By this way,the continuous thermal load model comprised by the environment basic temperature difference and continuous random one is set up.Using the thermal load model,the buckling and snap-through phenomena,the Pitchfork Bifurcation of plate are exhibited.Furthermore,the vibration characteristic of plate with varied aspect ratios is demonstrated and the responses at different representative nodes are compared.