時(shí)變材料中彈性波傳播特性研究
發(fā)布時(shí)間：2018-10-29 11:25
【摘要】：時(shí)間是描述物質(zhì)狀態(tài)的重要維度。性質(zhì)的時(shí)變性廣泛存在于相變材料、智能流體、基于可控人工細(xì)觀結(jié)構(gòu)的復(fù)合材料和處于極端物理?xiàng)l件下的材料中。然而在材料學(xué)中,材料的屬性通常被認(rèn)為是靜態(tài)或準(zhǔn)靜態(tài)的,在材料靜態(tài)性質(zhì)得到充分的研究之后,時(shí)變因素的考慮通常是理論研究的趨勢。因此前瞻性地將時(shí)間作為描述材料屬性的指標(biāo)具有重要的理論意義�；谛再|(zhì)時(shí)變過程滿足動(dòng)量守恒的假設(shè),本文建立了理想時(shí)變材料模型,并提出了其唯象的線彈性波動(dòng)研究方法。論文的主要研究內(nèi)容如下：1)提出時(shí)變介質(zhì)的若干基本假設(shè)。指出當(dāng)且僅當(dāng)時(shí)變介質(zhì)滿足動(dòng)量守恒假設(shè)時(shí),其線彈性動(dòng)力學(xué)問題可以直接采用經(jīng)典波動(dòng)方程進(jìn)行描述。2)分析材料屬性隨時(shí)間變化的特征并描述時(shí)變介質(zhì)中的性質(zhì)運(yùn)動(dòng)現(xiàn)象。證明材料屬性的時(shí)間和空間梯度會(huì)使相應(yīng)屬性發(fā)生與介質(zhì)本身的運(yùn)動(dòng)相互獨(dú)立的運(yùn)動(dòng),并指出性質(zhì)運(yùn)動(dòng)是時(shí)變介質(zhì)的顯著特征。推導(dǎo)性質(zhì)運(yùn)動(dòng)速度的公式,并基于性質(zhì)運(yùn)動(dòng)的概念提出用于描述介質(zhì)時(shí)-空不均勻性的理想模型——運(yùn)動(dòng)性質(zhì)界面。3)通過論證時(shí)變介質(zhì)不滿足頻率不變性指出模態(tài)分析方法不適用于研究時(shí)變介質(zhì)的彈性動(dòng)力學(xué)問題。波傳播方法沒有相關(guān)的限制,因此認(rèn)為波傳播方法是研究時(shí)變介質(zhì)彈性動(dòng)力學(xué)的理想方法。4)討論彈性波在一維和高維運(yùn)動(dòng)性質(zhì)界面?zhèn)鞑サ囊?guī)律。揭示運(yùn)動(dòng)性質(zhì)界面上的反射和折射(Snell)定律。分析界面運(yùn)動(dòng)對(duì)波傳播情形的影響并對(duì)不同情形進(jìn)行分類,討論每一類傳播情形的位移傳播系數(shù)。引入弱解思想來解決無法通過連續(xù)條件直接討論的情形。通過數(shù)值模擬驗(yàn)證上述分析得到的彈性波的位移傳播系數(shù)。分析性質(zhì)界面的運(yùn)動(dòng)和波速對(duì)傳播系數(shù)的影響。分析界面的運(yùn)動(dòng)對(duì)出射(包括反射和透射)彈性波的頻率、波長、傳播系數(shù)、機(jī)械能、全反射／凋落波的產(chǎn)生等的影響。討論在某些情形下,性質(zhì)界面運(yùn)動(dòng)激發(fā)沖擊波或引起負(fù)折射的現(xiàn)象。分析不同類別的情形傳播規(guī)律之間的聯(lián)系,最終可以得到兩個(gè)對(duì)稱性原理。5)將時(shí)間有序性引入結(jié)構(gòu)型復(fù)合材料并提出時(shí)-空超材料的概念。分析時(shí)-空超材料的可調(diào)性和“全帶”特性。改進(jìn)多尺度均質(zhì)化方法并使之適用于不滿足頻率不變性的彈性動(dòng)力學(xué)系統(tǒng)。基于改進(jìn)的多尺度均質(zhì)化方法討論時(shí)-空超材料的宏觀本構(gòu)。采用新的材料常數(shù)張量來描述時(shí)-空超材料,提出時(shí)-空超材料的彈性波動(dòng)方程并指出該方程非雙曲性的可能。提出時(shí)-空各向異性的概念,并用時(shí)-空各向異性來描述時(shí)-空超材料的波動(dòng)屬性。通過數(shù)值算例展示時(shí)-空各向異性的特征并通過數(shù)值模擬來驗(yàn)證時(shí)-空超材料的理論。
[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.
【學(xué)位授予單位】：西北工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O347.41
本文編號(hào)：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.
【學(xué)位授予單位】：西北工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O347.41
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相關(guān)期刊論文 前2條
1 南策文;從非常規(guī)復(fù)合效應(yīng)產(chǎn)生新型材料[J];自然科學(xué)進(jìn)展;2004年04期
2 胡海巖,郭大蕾,翁建生;振動(dòng)半主動(dòng)控制技術(shù)的進(jìn)展[J];振動(dòng)、測試與診斷;2001年04期
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