Thermal Modal Analysis Of Functionally Gradient Beam With Temperature-dependent Material Properties Based On Dynamic Poly-condensation

In any structural system,ranging from a few hundred meters or even tens of kilometers of the bridge system,and as small as only a few millimeters of vehicle collision beam,beam structure is an indispensable structural as one of the important components.At present,the function of gradient materials is important of all ages about the researchers by the virtue of its excellent thermal shock,corrosion resistance,oxidation resistance and wear resistance.In order to meeting the different requirements of different structures on the beam,the research of FGM beams has become a development trend of today's beam structure.In this paper,the thermal modal analysis of FGM beams composed of two kinds of materials,1100 Al and ZrO₂,is carried out based on small deformation geometric nonlinear theory and dynamic poly-condensation method.Firstly,the finite element method of FGM beams is deduced according to the finite element method.And the computational complexity is reduced by the dynamic poly-condensation method.Then,the results of the dynamic poly-condensation are analyzed by the compare of finite element method and the exact solution of the analytical method.The correctness of the dynamic poly-condensation method and the accuracy of the calculation are tested.Finally,the variation law of the distribution coefficient and the porosity control parameters of the different components FGM beams under different temperature and different displacement boundary conditions are analyzed.In this paper,the effects of composition,porosity,and displacement boundary conditions and temperature on the natural frequency of the beam are investigated.When the temperature is constant,the natural frequency of the FGM beam is increasing with the increase of the component parameters.This is because the composition of ZrO₂ increases with the increase of the component parameters.And the natural frequency of the FGM beam increases with the increase of the porosity control coefficient,which indicates that the sensitivity of the porosity control coefficient to the density is higher than that of the stiffness.When the component parameters and porosity control coefficient are constant,the natural frequency of the beam decreases with the increase of temperature,This is because of the thermal stress in the beam reducing the stiffness of the beam,and resulting the decrease of its natural frequency.In this paper,the thermal modal analysis of the FGM beam provides a theoretical basis for the dynamic analysis of the FGM beam,which provides a reference value for the engineering application of the FGM beam.