本文選題：顆粒鏈 + 高度非線性孤立波��； 參考：《西安理工大學(xué)》2017年碩士論文

【摘要】：一維顆粒鏈?zhǔn)且环N特殊的介質(zhì),一維顆粒鏈中包含著線性、弱非線性以及強(qiáng)非線性動(dòng)態(tài)響應(yīng),其中,強(qiáng)非線性動(dòng)態(tài)響應(yīng)使得顆粒鏈?zhǔn)芘鲎埠螽a(chǎn)生一種應(yīng)力波——高度非線性孤立波,孤立波的穩(wěn)定性強(qiáng),可控性好,是一種非常好的信息載體。功能梯度材料(Functionally graded materials, FGM)是一種新型材料,功能梯度材料的材料要素(組成、結(jié)構(gòu))沿某一方向呈現(xiàn)連續(xù)梯度變化,其材料屬性在該方向上也呈現(xiàn)連續(xù)變化的狀態(tài),功能梯度材料廣泛應(yīng)用在航空航天領(lǐng)域中,研究人員致力于研究其力學(xué)特性以及結(jié)構(gòu)優(yōu)化設(shè)計(jì)。一維顆粒鏈?zhǔn)艿阶矒艉髸a(chǎn)生穩(wěn)定的孤立波,基于高度非線性孤立波對彈性大板的健康診斷和無損檢測理論,研究一維顆粒鏈和功能梯度材料的耦合作用,全面探究反射孤立波對與之直接接觸的功能梯度材料的材料屬性、幾何構(gòu)型的敏感程度。本文以一維顆粒鏈中的高度非線性孤立波為信息載體,將功能梯度材料作為與之直接接觸的結(jié)構(gòu)體,研究一維顆粒鏈與功能梯度材料的耦合作用,并進(jìn)行建模和仿真分析,主要研究內(nèi)容如下:1、介紹顆粒以及顆粒鏈的性質(zhì):基于牛頓擺引出特殊的介質(zhì)——顆粒鏈,通過顆粒以及顆粒鏈的性質(zhì),引出本文所要研究的主要內(nèi)容;基于赫茲接觸定律推導(dǎo)顆粒與不同幾何構(gòu)型的結(jié)構(gòu)體作用時(shí),壓縮量與接觸力的關(guān)系。確定顆粒的數(shù)量和顆粒的材料屬性,基于經(jīng)典牛頓定律推導(dǎo)一維顆粒鏈和功能梯度材料耦合作用的待定方程組。2、研究一維顆粒鏈與半無限功能梯度結(jié)構(gòu)體的耦合作用:基于Hertz接觸定律和梯度半空間接觸問題下荷載與壓入深度的關(guān)系,通過牛頓第二定律,建立一維顆粒鏈與半無限功能梯度結(jié)構(gòu)體耦合作用的微分方程組,并采用四階Runge-Kutta法求解。得到不同彈性模量和梯度參數(shù)下中間顆粒的速度曲線和各個(gè)顆粒的位移曲線,分析結(jié)構(gòu)體的彈性模量和梯度參數(shù)對回彈孤立波的影響。3、研究一維顆粒鏈與功能梯度薄板的耦合作用:基于Hertz定律、梯度半空間接觸問題下荷載與壓入深度的關(guān)系,通過牛頓第二定律以及板的內(nèi)在非彈性理論,建立一維顆粒鏈與功能梯度薄板耦合作用的微分方程組,并采用四階Runge-Kutta法求解。分別得到五個(gè)不同物性參數(shù)下中間顆粒的速度曲線和各個(gè)顆粒的位移曲線,分析功能梯度薄板的物性參數(shù)在其變化范圍內(nèi)對回彈孤立波的影響。4、對接觸和碰撞過程進(jìn)行建模與仿真分析:對單個(gè)顆粒和半無限均質(zhì)材料的接觸過程進(jìn)行有限元仿真分析;對一維顆粒鏈和半無限均質(zhì)材料碰撞過程進(jìn)行有限元仿真分析。
[Abstract]:One-dimensional particle chain is a special medium, which contains linear, weakly nonlinear and strongly nonlinear dynamic responses. Because of the strong nonlinear dynamic response, a kind of stress wave-high nonlinear solitary wave is produced after the particle chain is collided. The solitary wave has strong stability and good controllability. It is a very good information carrier. Functional graded materials (FGM) is a new type of material. The material elements (composition, structure) of functionally graded materials (FGM) show continuous gradient changes along a certain direction, and the material properties of FGM also show continuous changes in that direction. Functionally graded materials (FGM) are widely used in aeronautics and astronautics. Researchers focus on their mechanical properties and structural optimization design. One dimensional particle chain will produce stable solitary waves after impact. Based on the health diagnosis and nondestructive testing theory of high nonlinear solitary waves, the coupling effect between one-dimensional particle chains and functionally graded materials is studied. The sensitivity of reflective solitary waves to the material properties and geometric configurations of functionally graded materials in direct contact with them is investigated. In this paper, the highly nonlinear solitary wave in one-dimensional particle chain is used as the information carrier, and the functionally graded material is taken as the structure directly in contact with it. The coupling effect between the one-dimensional particle chain and the functionally graded material is studied, and the modeling and simulation are carried out. The main research contents are as follows: 1. The properties of particles and their chains are introduced. Based on Newtonian pendulum, the special media-particle chain is introduced, and the main contents of this paper are introduced by the properties of particles and particle chains. Based on Hertz's contact law, the relation between the amount of compression and the contact force is derived for the interaction between particles and structures with different geometric configurations. Determine the number of particles and the material properties of the particles, Based on the classical Newton's law, the undetermined equations of one-dimensional particle chain and functionally graded material coupling are derived. The coupling between one-dimensional particle chain and semi-infinite functionally gradient structure is studied: based on Hertz's contact law and gradient half-space. The relationship between load and indentation depth under contact problem, By means of Newton's second law, the differential equations for the coupling of one-dimensional particle chains with semi-infinite functionally gradient structures are established and solved by the fourth-order Runge-Kutta method. The velocity curves of the intermediate particles and the displacement curves of each particle are obtained under different elastic modulus and gradient parameters. The influence of elastic modulus and gradient parameters on springback solitary wave is analyzed. The coupling effect of one-dimensional particle chain and functionally graded thin plate is studied. Based on Hertz's law, the relationship between load and indentation depth under gradient half-space contact problem is studied. By means of Newton's second law and the inner inelastic theory of plates, the differential equations of one-dimensional particle chain coupled with functionally graded thin plates are established and solved by the fourth-order Runge-Kutta method. The velocity curves of the intermediate particles and the displacement curves of each particle were obtained under five different physical parameters. The influence of physical parameters of functionally gradient thin plate on springback solitary wave is analyzed. The contact and collision processes are modeled and simulated. The contact process of single particle and semi-infinite homogeneous material is simulated by finite element method. The collision process of one-dimensional particle chain and semi-infinite homogeneous material is simulated by finite element method.
【學(xué)位授予單位】：西安理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB34;O34

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