时变材料中弹性波传播特性研究
发布时间：2018-10-29 11:25
【摘要】：时间是描述物质状态的重要维度。性质的时变性广泛存在于相变材料、智能流体、基于可控人工细观结构的复合材料和处于极端物理条件下的材料中。然而在材料学中,材料的属性通常被认为是静态或准静态的,在材料静态性质得到充分的研究之后,时变因素的考虑通常是理论研究的趋势。因此前瞻性地将时间作为描述材料属性的指标具有重要的理论意义。基于性质时变过程满足动量守恒的假设,本文建立了理想时变材料模型,并提出了其唯象的线弹性波动研究方法。论文的主要研究内容如下：1)提出时变介质的若干基本假设。指出当且仅当时变介质满足动量守恒假设时,其线弹性动力学问题可以直接采用经典波动方程进行描述。2)分析材料属性随时间变化的特征并描述时变介质中的性质运动现象。证明材料属性的时间和空间梯度会使相应属性发生与介质本身的运动相互独立的运动,并指出性质运动是时变介质的显著特征。推导性质运动速度的公式,并基于性质运动的概念提出用于描述介质时-空不均匀性的理想模型——运动性质界面。3)通过论证时变介质不满足频率不变性指出模态分析方法不适用于研究时变介质的弹性动力学问题。波传播方法没有相关的限制,因此认为波传播方法是研究时变介质弹性动力学的理想方法。4)讨论弹性波在一维和高维运动性质界面传播的规律。揭示运动性质界面上的反射和折射(Snell)定律。分析界面运动对波传播情形的影响并对不同情形进行分类,讨论每一类传播情形的位移传播系数。引入弱解思想来解决无法通过连续条件直接讨论的情形。通过数值模拟验证上述分析得到的弹性波的位移传播系数。分析性质界面的运动和波速对传播系数的影响。分析界面的运动对出射(包括反射和透射)弹性波的频率、波长、传播系数、机械能、全反射／凋落波的产生等的影响。讨论在某些情形下,性质界面运动激发冲击波或引起负折射的现象。分析不同类别的情形传播规律之间的联系,最终可以得到两个对称性原理。5)将时间有序性引入结构型复合材料并提出时-空超材料的概念。分析时-空超材料的可调性和“全带”特性。改进多尺度均质化方法并使之适用于不满足频率不变性的弹性动力学系统。基于改进的多尺度均质化方法讨论时-空超材料的宏观本构。采用新的材料常数张量来描述时-空超材料,提出时-空超材料的弹性波动方程并指出该方程非双曲性的可能。提出时-空各向异性的概念,并用时-空各向异性来描述时-空超材料的波动属性。通过数值算例展示时-空各向异性的特征并通过数值模拟来验证时-空超材料的理论。
[Abstract]:Time is an important dimension to describe the state of matter. The time-varying properties are widely used in phase change materials, intelligent fluids, composites based on controllable microstructures and materials under extreme physical conditions. However, in materials science, the properties of materials are usually regarded as static or quasi-static, and the consideration of time-varying factors is usually the trend of theoretical research after the static properties of materials are fully studied. Therefore, it is of great theoretical significance to prospectively regard time as an index to describe the properties of materials. Based on the assumption that the properties of time-varying processes satisfy the conservation of momentum, an ideal time-varying material model is established in this paper, and a phenomenological method for the study of linear elastic waves is proposed. The main contents of this paper are as follows: 1) some basic assumptions of time-varying medium are proposed. It is pointed out that if and only if the time-varying medium satisfies the momentum conservation hypothesis, The linear elastic dynamics problem can be described directly by classical wave equation. 2) the characteristics of material properties changing with time are analyzed and the property motion phenomena in time-varying medium are described. It is proved that the temporal and spatial gradients of material attributes make the corresponding properties move independently from the motion of the medium itself, and it is pointed out that the property motion is a significant feature of time-varying medium. Deducing the formula of the property of the velocity of motion, Based on the concept of property motion, an ideal model for describing the time-space inhomogeneity of medium is proposed. 3) it is pointed out that the modal analysis method is not suitable for research by demonstrating that time-varying medium does not satisfy the frequency invariance. The elastic dynamics of time-varying medium is studied. The wave propagation method is considered to be an ideal method for studying the elastic dynamics of time-varying media. 4) the law of elastic wave propagation at the interface of one and high dimensional motion is discussed. The (Snell) law of reflection and refraction on the moving interface is revealed. The influence of interface motion on wave propagation is analyzed and the displacement propagation coefficients of each case are discussed. The idea of weak solution is introduced to solve the situation which can not be discussed directly by continuous condition. The displacement propagation coefficient of elastic wave is verified by numerical simulation. The effects of the motion of the interface and the velocity of the wave on the propagation coefficient are analyzed. The effects of interface motion on the frequency, wavelength, propagation coefficient, mechanical energy, total reflection / withered wave generation of elastic waves (including reflection and transmission) are analyzed. In some cases, the phenomena of shock wave or negative refraction caused by the motion of the property interface are discussed. Two symmetry principles can be obtained by analyzing the relationship between the propagation laws of different kinds of cases. 5) the time ordering is introduced into structural composites and the concept of time-space supermaterial is put forward. The tunability and "full band" properties of time-space supermaterials are analyzed. The method of multiscale homogenization is improved and applied to elastodynamic systems which do not satisfy the frequency invariance. Based on the improved multi-scale homogenization method, the macroscopic constitutive structure of time-space supermaterial is discussed. A new material constant Zhang Liang is used to describe the space-time supermaterial. The elastic wave equation of the time-space supermaterial is proposed and the possibility of nonhyperbolic property of the equation is pointed out. The concept of time-space anisotropy is proposed and the fluctuation properties of time-space supermaterials are described by time-space anisotropy. The characteristics of time-space anisotropy are demonstrated by numerical examples and the theory of time-space supermaterial is verified by numerical simulation.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O347.41
本文编号：2297564
[Abstract]:Time is an important dimension to describe the state of matter. The time-varying properties are widely used in phase change materials, intelligent fluids, composites based on controllable microstructures and materials under extreme physical conditions. However, in materials science, the properties of materials are usually regarded as static or quasi-static, and the consideration of time-varying factors is usually the trend of theoretical research after the static properties of materials are fully studied. Therefore, it is of great theoretical significance to prospectively regard time as an index to describe the properties of materials. Based on the assumption that the properties of time-varying processes satisfy the conservation of momentum, an ideal time-varying material model is established in this paper, and a phenomenological method for the study of linear elastic waves is proposed. The main contents of this paper are as follows: 1) some basic assumptions of time-varying medium are proposed. It is pointed out that if and only if the time-varying medium satisfies the momentum conservation hypothesis, The linear elastic dynamics problem can be described directly by classical wave equation. 2) the characteristics of material properties changing with time are analyzed and the property motion phenomena in time-varying medium are described. It is proved that the temporal and spatial gradients of material attributes make the corresponding properties move independently from the motion of the medium itself, and it is pointed out that the property motion is a significant feature of time-varying medium. Deducing the formula of the property of the velocity of motion, Based on the concept of property motion, an ideal model for describing the time-space inhomogeneity of medium is proposed. 3) it is pointed out that the modal analysis method is not suitable for research by demonstrating that time-varying medium does not satisfy the frequency invariance. The elastic dynamics of time-varying medium is studied. The wave propagation method is considered to be an ideal method for studying the elastic dynamics of time-varying media. 4) the law of elastic wave propagation at the interface of one and high dimensional motion is discussed. The (Snell) law of reflection and refraction on the moving interface is revealed. The influence of interface motion on wave propagation is analyzed and the displacement propagation coefficients of each case are discussed. The idea of weak solution is introduced to solve the situation which can not be discussed directly by continuous condition. The displacement propagation coefficient of elastic wave is verified by numerical simulation. The effects of the motion of the interface and the velocity of the wave on the propagation coefficient are analyzed. The effects of interface motion on the frequency, wavelength, propagation coefficient, mechanical energy, total reflection / withered wave generation of elastic waves (including reflection and transmission) are analyzed. In some cases, the phenomena of shock wave or negative refraction caused by the motion of the property interface are discussed. Two symmetry principles can be obtained by analyzing the relationship between the propagation laws of different kinds of cases. 5) the time ordering is introduced into structural composites and the concept of time-space supermaterial is put forward. The tunability and "full band" properties of time-space supermaterials are analyzed. The method of multiscale homogenization is improved and applied to elastodynamic systems which do not satisfy the frequency invariance. Based on the improved multi-scale homogenization method, the macroscopic constitutive structure of time-space supermaterial is discussed. A new material constant Zhang Liang is used to describe the space-time supermaterial. The elastic wave equation of the time-space supermaterial is proposed and the possibility of nonhyperbolic property of the equation is pointed out. The concept of time-space anisotropy is proposed and the fluctuation properties of time-space supermaterials are described by time-space anisotropy. The characteristics of time-space anisotropy are demonstrated by numerical examples and the theory of time-space supermaterial is verified by numerical simulation.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O347.41
【参考文献】
相关期刊论文 前2条
1 南策文;从非常规复合效应产生新型材料[J];自然科学进展;2004年04期
2 胡海岩,郭大蕾,翁建生;振动半主动控制技术的进展[J];振动、测试与诊断;2001年04期
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