【作者】 王迪；

【导师】 朱翔；

【作者基本信息】 华中科技大学 ， 船舶与海洋结构物设计制造， 2017， 硕士

【摘要】 工程结构在服役期间会出现各种形式的损伤,其结构动力学参数和能量传播形式也会随之产生一定的变化,因此基于振动的结构损伤识别得到了广泛的研究并且在实际工程运用中得到应用。能量有限元法(EFEA)是近些年发展起来的一种研究结构中高频振动响应的数值分析方法。该方法以能量密度作为声振系统的动力控制方程的基本变量,将能量看作是以波动的形式在结构中进行传递,同时以有限元的形式离散结构单元,一方面可以表达出结构的几何特性,另一方面也可以充分展现结构的阻尼特性。它结合了统计能量法(SEA)和传统有限元法(FEA)的优点,是一种混合建模分析技术。本文首先针对普通梁推导了梁的能量密度控制方程,得到了结构中能量密度和能量流的表达式。将损伤单元的效应通过弹性模量和阻尼的变化引入到能量有限元分析模型中,分析了损伤梁结构并将梁的能量有限元应用于损伤结构的振动分析中。针对损伤结构,提出基于能量密度和能量流变化的两个损伤指标,对损伤识别指标进行了可视化分析,算例分析表明能量密度和能量流差对于结构中的损伤比较敏感,基于结构能量流变化的指标更能有效地识别结构损伤。随后根据能量守恒定律,推导了耦合梁结构的能量密度方程,并对耦合梁结构做了进一步的损伤分析。在梁结构能量有限元的理论基础上,针对普通板建立了板的能量密度控制方程,推导了板结构能量密度和结构声强的表达式,同时利用能量守恒定律建立了耦合板的能量密度方程。随后利用损伤单元弹性模量和阻尼的变化,对基于能量密度和结构声强变化的两个损伤指标进行了可视化的研究,通过损伤板的算例确定了基于结构声强变化的指标更能有效地识别板结构的损伤。然后基于能量有限元法对功能梯度材料梁和功能梯度板进行了振动分析。假设功能梯度材料参数随厚度方向指数变化,考虑功能梯度梁和板中的弯曲振动,分别推导了功能梯度梁和板振动的能量密度控制方程,并推导了耦合梁和耦合板中弯曲波运动的能量有限元连接矩阵,从而建立了功能梯度耦合梁和耦合板结构的能量有限元方程,计算了功能梯度耦合梁和耦合板中的能量密度和结构声强。考虑到功能梯度梁和板中的损伤,分析了损伤功能梯度梁和板的振动,并利用基于结构声强变化的损伤指标对功能梯度材料结构进行了损伤识别分析。本文的研究对梁和板结构以及功能梯度材料梁板结构中的损伤识别提供了新的方法,并通过构造功能梯度梁、板的能量有限元方程,为基于能量有限元法的功能梯度结构振动分析提供了理论基础。更多还原

【Abstract】 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.更多还原