【作者】 刘明；

【导师】 程远胜；

【作者基本信息】 华中科技大学 ， 船舶与海洋结构物设计制造， 2015， 博士

【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。更多还原

【Abstract】 Functionally graded materials (FGMs) are usually made from a mixture of metals and ceramics which vary continuously and gradually over volume in composition and microstructure. In spite of microscopically inhomogeneous, FGMs are macroscopically homogeneous composites. These advantages help to reduce mechanically and thermally induced stresses caused by the material property mismatch and to improve the bonding strength. Therefore, FGMs are usually applied in the sandwich plates and shells to improve the bonding strength between the core and the face sheets and to reduce mechanically and thermally induced stresses caused by the material property mismatch between the core and the face sheets. Because the vibration behavior is an important indictor to characterize the structure performance, the research on the vibration of FGM sandwich plates and shells has significant theoretical value and practical value.This thesis studies the free vibration of several novel types of FGM sandwich plates and shells with flexible core by using high order sandwich plane theory (HSAPT), including:sandwich plate with both functionally graded face sheets and functionally graded flexible core, sandwich plate with bilinearly graded flexible core, grid stiffened sandwich plate with flexible functionally graded material filled, submerged composite sandwich cylindrical shell with functionally graded flexible core and grid stiffened sandwich cylindrical shell with flexible functionally graded material filled. The main works presented in the thesis are as follows:(1) Free vibration of sandwich plate with both functionally graded face sheets and functionally graded flexible core is studied by using refined high order sandwich plane theory. The properties of FGM follow a power-law function. The first order shear deformation theory is used for the face sheets and a3D-elasticity solution of weak core is employed for the core. The core layer has transverse normal and shear resistance only. On the basis of continuities of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are obtained by using Hamilton’s principle. The accuracy of the present approach is validated by comparing the analytical results obtained for a degradation model-sandwich plate with functionally graded face sheets and homogeneous flexible core with ones published in the literatures, as well as the numerical results obtained by finite element method and good agreements are reached. Then, parametric study is conducted to investigate the effect of distribution of functionally graded material properties, thickness to side ratio on the vibration frequencies.(2) Free vibration of sandwich plate with bilinearly graded flexible core is studied by using refined high order sandwich plane theory. The bilinearly graded flexible core is considered as two monotonically graded flexible core layers. As a result, the laminated two-layered core is analyzed and formulated by the mixed layer-wise theory. Then the sandwich plate is analyzed by combining the refined high order sandwich plane theory and the mixed layer-wise theory. In this way, the continuities of the displacements and stresses at the interfaces of face sheets and core, upper core layer and lower core layer are achieved. Meanwhile, the computation of this method is effectively reduced compared with the one by three dimensional theory and mixed layer-wise theory for the sandwich plate.(3) Free vibration of grid stiffened sandwich plate with flexible functionally graded material filled is studied. Due to the discontinuity between the materials of the ribs and the filler, the smear or homogenous method is usually used to study grid stiffened sandwich plate with filler in previous literature. This thesis introduces the discrete method to deal with the ribs. In addition, the material of the ribs is steel or other hard material so that the3D-elasticity solution of weak core cannot be used because the in-plane stresses cannot be neglected. Therefore, the both in-plane stresses and vertical stresses of the core are considered when using the high order sandwich plane theory. The classic thin plate theory is used for the face sheets. On the basis of continuities of the displacements at the interfaces of the face sheets and the core, Lagrange’s equations of motion are obtained by using Hamilton’s principle. Then the Chebyshev polynomials are adopted for the shape function and the frequency is solved by Ritz method.(4) Free vibration of submerged composite sandwich cylindrical shell with functionally graded flexible core is studied. The refined high order sandwich plane theory is employed for the structure while the wave propagation method is used to study the fluid-structure interaction. Assuming the wave travelling in the axial direction of the shell is approximately obtained by studying the wave travelling in a similar beam. Then the fluid loading can be obtained by the wave equation. Base on the continuity of the displacements at the interface of the outer face of the cylindrical shell and the fluid, equations of motion are obtained by using Hamilton’s principle.(5) Free vibration of grid stiffened sandwich cylindrical shell filling flexible functionally graded material is studied. The method employed for the structure is the same as the one for grid stiffened sandwich plate with flexible functionally graded material filled and the Lagrange’s equations of motion are derived. By using the Navier’s solution, the natural frequency of the grid stiffened sandwich cylindrical shell filling flexible functionally graded material is obtained.The thesis studies the free vibration of several novel FGM sandwich plates and shells with flexible core analytically. Different method is adopted depending on the type of the structure. New thoughts and methods are provided for studying the free vibration of novel FGM sandwich plates and shells with flexible core, which has a certain reference value for the further research and engineering design.更多还原