Statistical Behavior And Fatigue Life Prediction Of Random Dynamic Response Of Thin Plate Under Thermal Environment

During the flight of hypersonic flight vehicle in or out of the atmosphere,the fraction between vehicle body and the atmosphere will heat the vehicle,which causes destruction to the vehicle.So it is necessary to install thermal protection system(TPS)on the vehicle surface.Under the load of thermal environment and sonic,Gaussian or non-Gaussian response will occur on TPS,which propose challenges to the calculation of fatigue life.A composite panel on elastic foundation was constructed to describe the TPS of hypersonic vehicle.A multimode dynamic modal was built by Kirchhoff thin panel assumption and Von Kármán large deformation theory.A series of nonlinear dynamic equations were deduced using static condensation method and Galerkin method,and were integrated by four-order Runge-Kutta method.Dynamic response of the thin panel vibration were obtained.At the same time,a finite element model was established for simulation calculation.Both the theoretical formula and simulation showed that response of the thin panel under combined random acoustic pressure and thermal environment load might be Gaussian or non-Gaussian.Under the condition of low temperature load,the PDF of tranvese displacement and in-plane strain response of the thin plate under low sound pressure level were all Gaussian processes.Under the condition of high overall sound pressure level(OASPL),the symmetrical non-Gaussian distribution of displacement and deflective non-Gaussian distributed strain would occur.When subjected to higher temperature load,the response of the plate appeared intermittent or continuous snap-through motion,and the PDF of tranvese displacement appeared unequal bimodal distribution,and the PDF of in-plane strain appeared deflective bimodal distribution.When the temperature rise continued to increase,the sheet would vibrate around a large postbuckling displacement and nolonge snap-through.In addition,as the thermal protection system is spliced on the surface of the body,the gap between each TPS structure has a tight connection with the heat sealing material with a smaller module.Under the action of the heat sealing material,the boundary conditions are not ideal immobile boundaries,but rather elastic boundaries.Elastic boundary conditions will significantly affect the plate dynamic response behavior.In this paper,the elastic boundary was reduced to a smaller-module isotropic material.The influence of the elastic modulus of the boundary material on the dynamic response of the thin plate was calculated by finite element simulation.The results showed that the elastic modulus of the boundary material change the critical buckling temperature of the structure and the post-buckling displacement of the plate,thus affecting the dynamic response.Based on the above results of dynamic response,the fatigue damage was calculated.The time-domain rain flow method does not require that the strain is a Gaussian process,but a long-time response is needed to acquire a steady result.A frequency-domain method usually requires a Gaussian process,which is harsh to engineering.Therefore the frequency-domain Bendat method for a narrow-band response and the Dirlik method for a wide-band response with non-Gaussian corrective coefficient by Claudio formula have been used to estimate the fatigue damage.The results showed that when the response was a narrow-band process,the Bendat method needs to be used for calculation.The Dirlik method will result in less damage.When the response was a broad-band process,Dirlik method needs to be used for calculation.Bendat’s method is too conservative and can not be used.The non-Gaussian response process will increase the fatigue damage of the structure,which needs to be modified with Braccesi method to get the result close to rain flow counting result.