本文選題：復(fù)合材料 + 圓柱殼��； 參考：《太原理工大學(xué)》2015年碩士論文

【摘要】：隨著科技的進(jìn)步和加工工藝的日益革新，復(fù)合材料以其優(yōu)良的力學(xué)性能而廣泛的應(yīng)用于各類(lèi)工程結(jié)構(gòu)中，復(fù)合材料圓柱殼在動(dòng)態(tài)載荷作用下的力學(xué)行為是人們關(guān)注的重點(diǎn)。本文對(duì)復(fù)合材料圓柱殼在軸向階躍載荷作用下的力學(xué)行為進(jìn)行了詳細(xì)的討論，主要研究了圓柱殼的動(dòng)力屈曲和混沌行為。這些研究系統(tǒng)地揭示了復(fù)合材料圓柱殼在動(dòng)態(tài)載荷作用下的力學(xué)本質(zhì)，為其工程應(yīng)用提供了理論基礎(chǔ)。本文的研究工作主要包括以下幾個(gè)方面： （1）基于Hamilton原理和Donnell殼理論，考慮應(yīng)力波在殼中的傳播，得到了圓柱殼的動(dòng)力屈曲控制方程。利用Ritz法進(jìn)行求解，將動(dòng)力屈曲問(wèn)題轉(zhuǎn)化為一組齊次線性方程組的求解，，要使齊次線性方程組有非平凡解，則系數(shù)矩陣的行列式等于0，由此給出了屈曲長(zhǎng)度與屈曲臨界載荷曲線并得到了屈曲模態(tài)。利用MATLAB進(jìn)行編程計(jì)算，詳細(xì)討論了邊界條件、鋪層角度、環(huán)向模態(tài)數(shù)與軸向模態(tài)數(shù)等因素對(duì)復(fù)合材料圓柱殼的臨界屈曲載荷的影響。研究結(jié)果表明：圓柱殼在固支邊界條件下抵抗屈曲的能力最強(qiáng)，而圓柱殼在自由邊界條件下最容易發(fā)生屈曲，但是隨著應(yīng)力波的傳播，這一差異會(huì)逐漸減��；復(fù)合材料圓柱殼隨著徑厚比的增加，圓柱殼將更加容易出現(xiàn)高階模態(tài)。 （2）計(jì)及結(jié)構(gòu)變形的幾何非線性項(xiàng)，采用圓柱殼的非線性大撓度理論，基于應(yīng)力函數(shù)和Hamilton原理，得到了復(fù)合材料圓柱殼的大撓度控制方程。利用Ritz法和Galerkin法可得到單自由度的非線性動(dòng)力學(xué)控制方程。利用四階Runge-Kutta法進(jìn)行計(jì)算得到了系統(tǒng)的分叉圖、相平面和Poincaré映射，用此詳細(xì)的討論了系統(tǒng)的運(yùn)動(dòng)狀態(tài)，結(jié)果表明：復(fù)合材料圓柱殼的周期運(yùn)動(dòng)和混沌運(yùn)動(dòng)是隨著側(cè)向載荷幅值的增加而相互交替出現(xiàn)的。
[Abstract]:With the development of science and technology and the innovation of processing technology, composite materials are widely used in various engineering structures because of their excellent mechanical properties. The mechanical behavior of composite cylindrical shells under dynamic loading is the focus of attention. In this paper, the mechanical behavior of composite cylindrical shells under axial step loads is discussed in detail, and the dynamic buckling and chaotic behavior of cylindrical shells are studied. These studies systematically reveal the mechanical nature of composite cylindrical shells under dynamic loading and provide a theoretical basis for its engineering application. The research work of this paper mainly includes the following aspects: 1) based on Hamilton principle and Donnell shell theory, considering the propagation of stress wave in the shell, the governing equations of dynamic buckling of cylindrical shells are obtained. The dynamic buckling problem is transformed into the solution of a group of homogeneous linear equations by Ritz method. Then the determinant of the coefficient matrix is equal to 0, thus the buckling length and critical buckling load curve are obtained and the buckling modes are obtained. The effects of boundary condition, layer angle, toroidal mode number and axial mode number on the critical buckling load of composite cylindrical shells are discussed in detail by using MATLAB. The results show that the cylindrical shell has the strongest ability to resist buckling under the condition of clamped boundary, while the cylindrical shell is most prone to buckle under the free boundary condition, but the difference will gradually decrease with the propagation of stress wave. With the increase of the ratio of diameter to thickness, the higher modes of composite cylindrical shells will occur more easily. Taking into account the geometric nonlinear terms of structural deformation, the governing equations of large deflection of composite cylindrical shells are obtained by using the nonlinear large deflection theory of cylindrical shells and based on the stress function and Hamilton principle. The nonlinear dynamic control equations with single degree of freedom can be obtained by using Ritz method and Galerkin method. The bifurcation diagram, phase plane and Poincar 茅 map of the system are obtained by using the fourth-order Runge-Kutta method. The motion state of the system is discussed in detail. The results show that the periodic motion and chaotic motion of composite cylindrical shells alternate with the increase of lateral load amplitude.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：TB33

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