Vibration Analysis Of Damaged Structures Based On Energy Finite Element Method

While engineering structures served there will be cracks and other forms of damage,the structure dynamics parameters and the form of energy transmission will also change subsequently,so the research and identification of structural damage based on vibration is widely studied and is applied in engineering.Energy finite element method(EFEA)is a kind of numerical analysis method which has developed in recent years.This method is mainly based on the energy density which is the basic variable of the dynamic equation when the energy transfer in the structure as the wave at the same time.The structure is in the form of discrete finite element which can not only express the geometric characteristics of the structure but also show the damping characteristics.Overall,it is a hybrid modeling analysis technique which combines the advantages of the statistical energy method(SEA)and the traditional finite element method(FEA).In this paper,the beam's energy density control equation is formed with the expression of energy density and structural intensity.The effect of damage element is introduced into the finite element analysis model by the change of elastic modulus and damping,while analyzing the damage structure,EFEA is applied to the vibration analysis of the damaged structure.Aiming at the damage structure,two damage index is put forward based on the changes of energy density and energy flow with visual analysis,example shows that the energy density and energy flow difference is sensitive to the structure damage,but changes in the structure of energy flow index can be more effectively in structural damage identification.According to the law of energy conservation,the energy density equation of coupled beam structure is deduced and its damage analysis is also put forward.On the theoretical basis of energy beam structure finite element,the plate's energy density control equation is formed with the energy density and structural intensity.The energy density equation of coupled plates is also come into being by using the law of conservation of energy.With the help of the change of injury unit elastic modulus and damping,the two damage index of energy density and structural intensity changes are carried out based on the research of visualization.The structural intensity index is more effective in the recognition of plate structure damage by the example of plate.Based on the energy finite element method,the vibration analysis of functionally graded materials and functionally graded plates is carried out.Assuming that the functionally graded material parameters change with the thickness index,FGM beams and plates' s energy density control equation is formed.At the same time,the energy finite element connection matrix of bending wave motion in coupled beam and coupled plate is established.Considering the damage of functionally graded beams and plates,the vibration of functionally graded beams and plates is analyzed,and the damage identification of functionally graded materials is analyzed by using the damage index based on structural intensity changes.This study provides a new method for damage identification of beam and plate structure and functional gradient materials of beam and plate structure,with the energy finite element structure of FGM beam and plate equation,it provides the theoretical basis for functional gradient analysis of structural vibration based on finite element method.