The Improved Model For Vibrational Energy Flow Model And Its Applications In The Study Of Functionally Graded Structures

Aircraft,high-speed train and other large vehicles play important roles in economic development and the defense industry.In these mechanical systems,in order to achieve lightweight,high maneuverability and high speed,there usually exist a large number of thin-walled structures in the system,which will cause serious high-frequency vibration problems under the external broadband excitation.On the one hand,the high frequency vibration of the structure may cause fatigue damage of the parts,and thus affects the smooth operation and leads to the fatigue of the systems.On the other hand,the structure-borne sound radiation generated by the vibration of the structure can also produce noise pollution,which could affects the comfort of the operator.Therefore,it is of both theoretical and engineering values to predict and analyze the high frequency vibration of the structures,which is helpful to realize the optimization of the vibro-acoustic characteristics of such complex mechanical systems.The energy flow method is a high-frequency dynamic analysis method developed in recent years.This method is based on the governing equation of energy density,and it has unique advantages in predicting the spatial distribution characteristics of high-frequency responses of structures.However,for the high-frequency analysis of large vehicles such as high-speed train and aircraft,the existing structural energy flow methods have the defects of insufficient accuracy in some cases,and there is still a lack of corresponding models for various coupling forms of built-up structures in engineering.In addition,the existing structural energy flow models are suitable for uniform structures,whereas there is still a lack of corresponding theoretical models for functionally graded structures in large vehicles such as aircraft.Therefore,based on the shortcomings of the existing energy flow method and the basic principles of the method,this study developed the improved models to increase the prediction accuracy and broaden application range of the energ flow method.The energy flow method is then extended to the functionally graded structure,and the applicable range of this method is thus extended.The main research works of this paper are as follows:The energy transfer relation,energy dissipation relation and power input relation in the energy flow method of one-dimensional beam structure were studied theoretically.The applicable conditions of each hypothesis,and the physical nature of the energy flow method of beam structure were clarified.The influences of excitation frequency and damping loss factor on the accuracy of energy flow method for beam structure were studied.On this basis,the mobility correction method of beam structure based on wave-based method was proposed to extend its application scope,so that the energy flow model of beam structure can also be applied to a single excitation frequency.In order to analyze the high frequency vibration responses of coupled beam structures in mechanical system,the energy flow model of coupled beam structure with elastic joints was established.At the same time,considering the the longitudinal wave and flexural wave of the coupled beams simultaneously,the method for calculating the energy transfer coefficients at the elastic connection of coupled beams was established.The energy transmission characteristics of joint in couple beams when subjected to flexural and axial loadings were investigated,and the influences of coupling angle,joint stiffness and excitation frequency on the energy transfer characteristics were studied.Based on the study of the physical nature of the energy flow model of one-dimensional beam structure,an energy flow method for high frequency analysis of elastic coupled beams was proposed by using the energy transfer coefficient.The physical nature of energy flow model of two-dimensional plate structure was studied,and the error source of existing energy flow model of plate structure was identified.It is shown that the excitation frequency,the characteristic size of the plate and the damping loss factor are the key factors affecting the prediction accuracy of the plate's energy flow model,and the neglecting of the direct field is the main reason for the error of the energy flow model in the two-dimensional plate structure.In order to improve the accuracy of the existing plate energy flow model,a hybrid method based on the superposition of direct field and reverberation field was proposed.The hybrid energy flow model of the plate was established by finite element discretization,so that the accuracy of the energy flow method was improved and the application range was sigificantly improved.The energy flow model of coupled plate was established,which is suitable forarbitary kinds of connections.The energy transfer characteristics of the coupled plate joints were analyzed by the energy transfer coefficient,and the influences of excitation frequency and coupling angle on the vibration energy transfer and conversion between the flexural wave,longitudinal wave and shear wave between were studied.Based on the study of the physical nature and error sources of the plate energy model,a hybrid energy flow analysis method for the coupled plate considering the influence of direct field and wave filtering effect of coupling boundary was established,which improved the accuracy of the results and extended the application range of the energy flow method in the analysis of the coupled plate structure.Based on the above research on the physical nature of the energy flow method for beam and plate structures,the energy flow method was then extended to the high-frequency vibration analysis of functionally graded structures.The energy flow models for functionally graded beams and functionally graded plates were established.At the same time,based on the engineering background that the functionally graded structures are often exposed in extreme thermal environment,considering the thermal stress generated by the extreme thermal environment and the change of the physical parameters of the functionally graded structure under extreme thermal environment,the energy flow model which can be applied to predict the high frequency response of the functionally graded beam and plate in extreme thermal environment were established.To sum up,the research works in this paper clarify the implementation principle,application range and error source of the energy flow method for the beam and plate.The corresponding improved models were proposed to improve the prediction accuracy and broaden application range of this method,which help to complete the theoretical basis of the energy flow method.In addition,in this study the applications of energy flow method were extended to functionally graded structure,which lays a foundation for the application of the energy flow method in the high-frequency analysis of large vehicle such as aircraft.