功能梯度材料软夹芯夹层板壳自由振动解析分析方法研究

发布时间：2018-01-06 22:24

本文关键词：功能梯度材料软夹芯夹层板壳自由振动解析分析方法研究　出处：《华中科技大学》2015年博士论文　论文类型：学位论文

【摘要】：功能梯度材料通常由金属和陶瓷混合而成,其在组成和微结构上随空间逐渐变化,在微观上是非均质,在宏观上却是均质的复合材料。这些优点可以有效地减小由于材料属性的不匹配导致的应力突变,并且提高粘合强度。因此,功能梯度材料常用于夹层板壳上,以提高夹层板壳芯层与面板之问的粘合强度及减小由于芯层与面板材料属性不匹配导致的应力突变。结构的振动特性是表征结构性能的重要指标之一,因此对功能梯度材料夹层板壳的振动研究具有重要的理论意义与实用价值。本文采用高阶夹层板理论研究了多种新型功能梯度材料软夹芯夹层板壳的自由振动,包括：面板和芯层同为功能梯度材料的软夹芯夹层板,双线性功能梯度材料软夹芯夹层板,软质功能梯度材料填充格栅增强夹层板,浸水功能梯度材料软夹芯复合材料夹层圆柱壳和软质功能梯度材料填充格栅增强夹层圆柱壳。主要研究工作包括： (1)对面板和芯层同为功能梯度材料的软夹芯夹层板的自由振动进行了解析分析方法研究。采用改进的高阶夹层板理论研究了其自由振动,功能梯度材料属性按照指数函数变化,面板采用一阶剪切理论而对于软芯层采用三维弹性解,仅考虑横向正应力和横向剪切应力,基于面板和芯层交界面处的位移和应力连续,利用哈密顿原理推导了运动方程。通过与参考文献中的退化模型-面板为功能梯度材料,芯层为均质软夹芯夹层板模型的理论结果进行对比,验证了方法的准确性。同时,对理论结果与有限元数值结果进行了对比,结果吻合很好。最后,进行了参数研究包括功能梯度材料属性的分布,厚度边长比对振动频率的影响。 (2)对双线性功能梯度材料软夹芯夹层板的自由振动特性进行了解析分析方法研究。由于其芯层是双线性的,因此认为其芯层是由两层单调梯度变化的软芯层组成。对层合的双芯层采用多层理论进行分析,对于整个夹层板的分析采用改进的高阶夹层板理论和多层理论相结合的方法,这样保证了面板与芯层界面,芯层与芯层界面的位移和应力的连续性,而且相对于三维理论和整体多层理论有效地降低了计算量。 (3)对于软质功能梯度材料填充格栅增强夹层板的自由振动进行了解析分析方法研究。由于栅格材料与填充材料的不一致,以往的文献通常采用平摊或者均质的理论方法来处理栅格,本文采用离散法对格栅加筋进行处理。另外,由于栅格采用的是钢质或者硬质材料,不能采用软芯层的处理方式,因此不能忽略芯层的面内应力,在采用高阶夹层板理论时芯层同时考虑面内应力和横向应力,面板采用薄板理论,基于面板和芯层界面处的位移连续,采用Hamilton原理建立了拉格朗日方程,而后假定Chebyshev多项式的形函数,采用李兹法进行求解。 (4)对浸水功能梯度材料软夹芯复合材料夹层圆柱壳的自由振动进行了解析分析方法研究。对于夹层圆柱壳采用改进的高阶夹层板理论,对于流体,采用波传播法,假定波在壳的轴向方向的传播近似于波沿梁轴向传播,通过波动方程,求得流体载荷,基于流体和圆柱壳外表面位移的连续性,采用哈密顿原理推导了运动方程。 (5)对软质功能梯度材料填充格栅增强夹层圆柱壳的自由振动进行了解析分析方法研究。圆柱壳采用与软质功能梯度材料填充格栅增强夹层板相同的方法,建立了拉格朗日运动控制方程。通过假定纳维叶解形式的形函数,求得软质功能梯度材料填充格栅增强夹层圆柱壳自由振动频率论文对多种功能梯度材料软夹芯夹层板壳的自由振动进行了理论分析,为功能梯度材料软夹芯夹层板壳的自由振动研究提供了新的研究思路和途径,对今后的理论研究和工程设计具有一定的参考价值。
[Abstract]:Functionally graded materials usually made of metal and ceramic mixture, its composition and microstructure gradually changes with space, in the micro is heterogeneous, composite material is homogeneous in the macro. These advantages can effectively reduce the material property mismatch stress due to the mutation, and therefore improve the bonding strength., functionally graded materials commonly used in sandwich shell, in order to improve the sandwich shell core layer and the panel asked the bonding strength of the core layer and the panel and reduce the material property mismatch stress due to the mutation. The vibration characteristics of structure is one of the important indexes characterizing the structure and properties, so the research on vibration of functionally graded materials with sandwich shell the theoretical significance and practical value.
This paper uses high order sandwich plate theory, the free vibration of a variety of new functional gradient material soft sandwich shell of the study includes: the panel and core layer with FGM soft sandwich plate, bilinear functional gradient material soft sandwich plate, soft FGM filled geogrid reinforced sandwich plate, soaking FGM soft sandwich composite sandwich cylindrical shell and soft FGM filled geogrid reinforced sandwich cylindrical shell. The main research work includes:
(1) of the panel and core layer with FGM sandwich soft sandwich plate free vibration was studied. By analysis of improved high order sandwich plate theory the free vibration study of functionally graded materials properties of the exponential function change, using the first-order shear panel theory for soft core by the three-dimensional elastic solution, only considering transverse normal stress and transverse shear stress, displacement of panel and core layer at the interface and stress continuity based on the equation of motion is derived by using the Hamilton principle. With the degradation model - panel in the reference for functional gradient materials, the core layer is compared with homogeneous soft sandwich laminate model theoretical results, verify the accuracy of the method. At the same time, the theoretical results and numerical results were compared. The results are in good agreement. Finally, a parametric study was conducted including functionally graded material properties Distribution, the influence of the thickness of the thickness to the vibration frequency.
(2) on the free vibration characteristics of bilinear FGM sandwich plate of soft sandwich method of analysis. The core layer is bilinear, so that the core layer is composed of soft core layer two layer monotone gradient. Changes of dual core laminated layer by layer theory to analyze, for the sandwich plate were analyzed with the improved method of higher order sandwich plate theory and multi-layer combination of theory, so as to ensure the panel and core layer interface, the continuity of displacement of core layer and core layer interface and stress, but also relative to the three-dimensional theory and integrated multilayer theory can effectively reduce the amount of computation.
(3) for soft FGM filled geogrid reinforced sandwich plate for the free vibration analysis method of analysis. As the grid material and filling material is not the same, to deal with the previous literature usually grid method is used in flat or homogeneous, the dispersion method of geogrid reinforced processing. In addition, because the grid is used in steel or hard materials, can not be treated by the soft core layer, it can not ignore the in-plane stress of the core layer, the higher order sandwich plate theory core layer considering the in-plane stress and transverse stress, displacement of panel panel using thin plate theory, and the core layer at the interface is based on the continuous. The Lagrange equation is built using the Hamilton principle, and then assumed shape function of Chebyshev polynomials, the Ritz method is used to solve the problem.
(4) the free vibration of functionally graded materials immersed soft sandwich composite sandwich cylindrical shell was studied. Analytical analysis for sandwich cylindrical shell with improved high order sandwich plate theory for fluids, using the wave propagation method, assuming the propagation wave in the axial direction of the shell along the axial propagation approximation of Yu Bo beam, the fluctuation the equation of fluid loading, continuous fluid and outer surface of shells based on displacement, using the Hamiltonian principle deduced the equation of motion.
(5) of soft FGM filled geogrid reinforced free vibration of sandwich cylindrical shell was studied. Analysis of cylindrical shells with soft FGM filled geogrid reinforced sandwich plate in the same way, control equations are established by assuming that the solution of Navier Lagrange motion. The shape function form, obtained soft function gradient filling material of geogrid reinforced sandwich cylindrical shell vibration frequency
The free vibration of functionally graded materials of soft sandwich plate was analyzed, the research provides new ideas and approaches for the study of free vibration of functionally graded materials of soft sandwich plate, which has a certain reference value for further research and engineering design.

【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB34

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