具脱层复合材料梁动力特性研究

发布时间：2018-10-20 14:56

【摘要】：科学的发展推动了技术的提升,使得轻型、耐用的新型材料在工程中得到了广泛应用。而复合材料层合梁更由于具有比刚度大,比强度高及抗疲劳等诸多优点在工程领域更多重视。然而,由于复合材料层合结构由多相材料组成的,其在生产和使用过程中极易产生脱层。一方面脱层的存在,会导致结构的承载能力减小、刚度下降,进而影响结构安全和使用寿命;另一方面,梁使用中的非线性因素也对结构的安全和使用寿命产生重要影响。因此对具脱层复合材料梁结构进行非线性特性研究具有重要意义,能为复合材料结构的合理设计、控制非线性因素对结构的影响提供有益参考。首先,采用分区模型,利用弹性力学,复合材料力学,非线性力学的相关基本理论,建立了脱层梁的非线性运动控制微分方程。然后利用分离变量法,基于脱层的边界条件,脱层前沿的位移和力连续条件得到系统频率和模态函数。在数值研究中探讨了不同铺设角度、不同脱层深度、不同脱层长度及不同铺设材料等参数对梁自由振动频率和模态的影响。其次,利用Reissner变分原理,建立了含脱层复合材料层合梁的非线性运动控制方程,采用梁的振型本征函数,结合分离变量法、多尺度法对非线性常微分控制方程进行求解,,并探讨了不同脱层长度,脱层深度,铺设材料和外激励对具脱层梁结构主共振、超谐共振及亚谐共振幅频特性曲线的影响。最后,基于脱层梁的非线性动力学微分方程,利用四阶龙格-库塔法研究了具脱层复合材料梁在不同参数情况下的主共振以及脱层梁随激励幅值变化的分岔行为和混沌行为,并讨论了不同脱层长度、不同脱层深度下脱层梁分岔和混沌行为,揭示了脱层梁板结构的一些分岔与混沌运动规律。
[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.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O327;TB33

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