【摘要】：科學(xué)的發(fā)展推動了技術(shù)的提升,使得輕型、耐用的新型材料在工程中得到了廣泛應(yīng)用。而復(fù)合材料層合梁更由于具有比剛度大,比強(qiáng)度高及抗疲勞等諸多優(yōu)點(diǎn)在工程領(lǐng)域更多重視。然而,由于復(fù)合材料層合結(jié)構(gòu)由多相材料組成的,其在生產(chǎn)和使用過程中極易產(chǎn)生脫層。一方面脫層的存在,會導(dǎo)致結(jié)構(gòu)的承載能力減小、剛度下降,進(jìn)而影響結(jié)構(gòu)安全和使用壽命;另一方面,梁使用中的非線性因素也對結(jié)構(gòu)的安全和使用壽命產(chǎn)生重要影響。因此對具脫層復(fù)合材料梁結(jié)構(gòu)進(jìn)行非線性特性研究具有重要意義,能為復(fù)合材料結(jié)構(gòu)的合理設(shè)計(jì)、控制非線性因素對結(jié)構(gòu)的影響提供有益參考。首先,采用分區(qū)模型,利用彈性力學(xué),復(fù)合材料力學(xué),非線性力學(xué)的相關(guān)基本理論,建立了脫層梁的非線性運(yùn)動控制微分方程。然后利用分離變量法,基于脫層的邊界條件,脫層前沿的位移和力連續(xù)條件得到系統(tǒng)頻率和模態(tài)函數(shù)。在數(shù)值研究中探討了不同鋪設(shè)角度、不同脫層深度、不同脫層長度及不同鋪設(shè)材料等參數(shù)對梁自由振動頻率和模態(tài)的影響。其次,利用Reissner變分原理,建立了含脫層復(fù)合材料層合梁的非線性運(yùn)動控制方程,采用梁的振型本征函數(shù),結(jié)合分離變量法、多尺度法對非線性常微分控制方程進(jìn)行求解,,并探討了不同脫層長度,脫層深度,鋪設(shè)材料和外激勵對具脫層梁結(jié)構(gòu)主共振、超諧共振及亞諧共振幅頻特性曲線的影響。最后,基于脫層梁的非線性動力學(xué)微分方程,利用四階龍格-庫塔法研究了具脫層復(fù)合材料梁在不同參數(shù)情況下的主共振以及脫層梁隨激勵幅值變化的分岔行為和混沌行為,并討論了不同脫層長度、不同脫層深度下脫層梁分岔和混沌行為,揭示了脫層梁板結(jié)構(gòu)的一些分岔與混沌運(yùn)動規(guī)律。
[Abstract]:With the development of science and technology, light and durable materials are widely used in engineering. The composite laminated beam has many advantages, such as high specific stiffness, high specific strength and fatigue resistance. However, because the composite laminated structure is composed of multiphase materials, it is easy to produce delamination in the process of production and application. On the one hand, the existence of delamination will lead to the decrease of the bearing capacity and stiffness of the structure, which will affect the safety and service life of the structure. On the other hand, the nonlinear factors in the use of beams will also have an important impact on the safety and service life of the structure. Therefore, it is of great significance to study the nonlinear characteristics of composite beam structures with delamination, which can provide a useful reference for the rational design of composite structures and the control of the influence of nonlinear factors on the structures. Firstly, the nonlinear motion control differential equations of delaminated beams are established by using the basic theories of elastic mechanics, composite mechanics and nonlinear mechanics. Then the frequency and modal functions of the system are obtained based on the boundary condition of delamination and the continuous condition of displacement and force at the delamination front by using the method of separating variables. The effects of different laying angles, different delamination depths, different delamination lengths and different laying materials on the free vibration frequencies and modes of the beams are discussed. Secondly, using the Reissner variational principle, the nonlinear motion control equation of laminated beams with delamination is established. The vibration eigenfunction of the beam is adopted, and the method of separating variables is used. The nonlinear ordinary differential control equations are solved by multi-scale method. The effects of different delamination lengths, delamination depths, laying materials and external excitations on the main resonance, superharmonic resonance and subharmonic co-amplitude frequency characteristic curves of delaminated beams are discussed. Finally, based on the nonlinear dynamic differential equations of delaminated beams, the main resonance of delaminated composite beams with different parameters and the bifurcation behavior and chaotic behavior of delaminated beams with different parameters are studied by using the fourth order Runge-Kutta method. The bifurcation and chaotic behavior of delaminated beams with different delamination lengths and delamination depths are discussed, and some bifurcation and chaotic motion laws of delaminated beam-plate structures are revealed.
【學(xué)位授予單位】：長沙理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O327;TB33

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