Power Flow Finite Element Analysis To The Energy Transmission Of Arbitrary Plate And Coupled Structures

The vibration of the mechanical structure becomes a serious problem in the mechanical manufacturing industry. The vibration of not only influent the strength and the life of the machine, but also have bad influence to the manufacturers and customers in theirs body and psychology. So how to use the reasonable and efficient method to relieve the noise and vibration become urgent affairs in the mechanical industry. Meanwhile, the study on this problem appears more useful and important.The paper based on the National Science Foundation project (Number: 51275275) and the Middle-aged and the Young Scientists Award Foundation of Shandong Province (Number:BS2010ZZ006) and the cooperation project "Simulation and analysis to noise and vibration of the high speed train body". Compared with the tradition Finite Element Method (FEM) and Statistical Energy Analysis (SEA), Power Flow Finite Element Method (PFFEM) has large advantage on the high frequency vibration. This paper uses the PFFEM in the perspective of energy to analysis the vibration of structure. The main points and innovations as shown below:(1) The vibration control equation of the flexural wave, longitudinal wave and share wave in the thin plate have been given. The vibration displacement in the thin plate to the x, y, z direction also be derived here. Those results are very important to calculate power transmission coefficient of the coupled structure. Then based on the energy balance differential equation, we have done the numerical simulation to the plate vibration by using the PFFEM.(2) Based on the PFFEM, by cooperating the traditional iso-parametric element in the FEM with the Delaunary triangulation arithmetic to do the flexural vibration analysis of the 1/4 disc structure, the whole disc structure and circular plate. Combined the ANSYS with MATLAB to do the PFFEM analysis of arbitrary shaped plate. What’s more, compared the result of FEM and PFEM.(3) The vibration displacements to the direction of x, y, z in L-shaped and arbitrary angle coupled plates are derived when the flexural wave, longitudinal wave and shear wave as incident wave respectively. Based on the result, the energy transmission coefficient of those three types wave have been calculated. Meanwhile, the paper discussed the variation rule of wave changing and transmission coefficient with the incident wave angle, plate thickness and incident wave frequency. The result shows the plate height has great influence on the wave changing. The effect of longitudinal wave and shear wave in plane can’t be neglected. Then the paper also discussed the variation rule of transmission coefficient with the coupled structure angle.(4) The vibration numerical simulation of the arbitrary angle coupled structure is studied by using the PFFEM. What’s more, we have attained the conclusion that the plate vibration is approximate to the vibration of the large angle coupled plates. These results offer the theoretical guidance to the engineering problem in practice.