High Frequency Vibration Analysis Method For Functionally Graded Materials Plate And Beam Coupled Structures

In the primary stage of structure design,the vibration characteristic response analysis of the structure is carried out by using the numerical information prediction analysis technology,which can reduce the noise and vibration level of the system structure at different frequencies,which is a very important link in the structural design stage.There is a very important relationship between the analysis method and the excitation frequency in the process of structural vibration propagation.At present,numerical analysis technology has been widely used in structural vibration analysis and design stage.The amplitude and phase of different excitation frequencies are used to represent the structural vibration characteristics.However,in the high frequency range,the traditional numerical analysis methods can not accurately capture the structural vibration characteristics.In order to achieve the purpose of structural vibration reduction and noise reduction,based on the wave theory,the energy flow analysis method is used to study the energy transfer path of structure vibration under high frequency excitation.Because of its special design performance,FGM has been widely used in various fields.As the most basic components in engineering application,the high frequency vibration response analysis of plate,beam and their coupled structures is more practical.Therefore,this paper studies the acoustic vibration characteristics and fluid structure coupled characteristics of FGM plate beam coupled structure under high frequency excitation.In order to establish a method for high frequency vibration analysis of functionally graded beam structures based on energy flow response,based on Euler-Bernoulli beam theory,according to the structural characteristics of functional graded beam structure,the energy balance equation of functionally gradient beam structure is established.Combined with Galerkin weighted residual method,the energy finite element analysis model of functional gradient beam structure is established.The results of numerical examples show that the energy transfer path of FGM beam under high frequency excitation and and the influence of different damping factors and material volume ratio on structural energy loss.In order to establish a high-frequency vibration response analysis method of functionally graded stiffened plate structure based on energy finite element analysis,the relationship between sound intensity and energy density after space-time average processing and far-field approximation assumption is established by using thin plate theory.Then,the energy density governing equation of functionally graded plate is derived.The stiffened plate structure is simplified as a plate beam coupling structure.The energy transfer coefficient is derived from the principle of flow continuity,and the model is solved by programming with MATLAB software.The energy density distribution of stiffened plate under different working conditions is obtained by example analysis,and the influence of stiffener on energy transfer is studied.In order to establish an energy finite element analysis method for high frequency vibration response of functionally graded plate structure in contact with mean flow,the hydrodynamic pressure model is established by using the velocity potential function and Bernoulli equation,and the energy density control equation is derived by considering the bending wave number of plates along the bending wave and mean flow direction.The numerical analysis of the simple plate and the coupled plate under several excitation frequencies is carried out and compared with the analytical solution to verify the correctness of the model.In order to establish a high-frequency vibration analysis method for functionally graded stiffened plate structures with one-sided fluid contact based on energy finite element analysis,the additional mass effect and radiation damping effect caused by fluid load are considered in the derivation of the control differential equation of EFEA.In addition,the fluid load effect and the existence of stiffeners are taken into account in the energy transfer coefficient of the coupling between stiffeners and stiffeners.The numerical example shows that the model can capture the response characteristics of the structure well.