【作者】 张玲；

【导师】 朱翔；

【作者基本信息】 华中科技大学 ， 船舶与海洋结构物设计制造， 2016， 硕士

【摘要】 功能梯度材料是由两种或以上不同性质的材料沿空间通过连续改变组分而形成,具有抗高温、韧性好、强度高等优点,在航天、能源、机械、国防等领域应用广泛。其接结构力学研究已是当今力学研究的一个重要方向。本文系统研究了功能梯度材料板壳结构在空气中的振动与声学特性。本文首先研究了四边简支边界条件下功能梯度矩形板自由振动特性。基于经典薄板理论,忽略剪切变形的影响,假定振型函数求取结构自由振动固有频率。在此基础上,研究功能梯度矩形板受迫振动功率流特性。采用模态叠加法获得矩形板受迫振动响应位移,继而通过可视化方法得到振动功率流强度矢量图和流线图。接着,分别建立有障板与无障板两种条件下功能梯度矩形板声学模型并分析其声辐射特性。根据Rayleigh积分公式获得有障板功能梯度矩形板远场声压,再利用阻抗矩阵求解辐射声功率。利用Green函数推导无障板功能梯度矩形板声压表达式,从而求解其辐射声功率。并将两种条件下功能梯度矩形板声辐射特性进行对比分析,考察障板对结构声辐射的影响。最后讨论了两端简支功能梯度圆柱壳自由振动特性。基于经典薄壳理论,忽略剪切变形的影响,得到壳体自由振动固有频率解。同时考虑内压对壳体自由振动的影响,并且基于内压与壳体固有频率关系提出了预报功能梯度圆柱壳弹性失稳临界压力的方法。更多还原

【Abstract】 Functionally graded materials(FGMs) are composed of two or more materials through continuously changing its fractions along dimension. FGMs have the advantages of high temperature resistance, good toughness, high strength and so on, so they have been widely used in aerospace, energy, machinery, defense and other fields. The mechanical behavior of functionally graded material structures is an important direction in mechanics research fields. The vibration and acoustic characteristics of functionally graded plates and shells in air are studied in this thesis.First, the free vibration characteristics of an functionally graded rectangular plate with simply supported boundary conditions are studied. Based on the classical thin plate theory and by ignoring the influence of the shear deformation, the natural frequency is obtained by assuming the modal function. On the basis of the above study, the power flow characteristics of FG rectangular plate under harmonic excitation are analyzed. The flexural displacement is solved by modal superposition method, then the power flow vector and flow maps are obtained by visualization method.Second, the models of baffled and unbaffled FG rectangular plates are set up and the acoustic characteristics are analyzed. According to the Rayleigh integral formula, the far field sound pressure of a baffled FG rectangular plate is obtained, then the radiated sound power is solved by impedance matrix. Through the Green function, the sound pressure and radiated sound power of an unbaffled FG rectangular plate are obtained. The influence of baffle on acoustic characteristics are discussed by comparing the results.Finally, the free vibration characteristics of a functionally graded cylindrical shell with simply supported ends are obtained. Based on the classical thin shell theory and ignored the influence of the shear deformation, the natural frequency is obtained by assuming modal function. Considering the influence of internal pressure, the free vibration characteristics of a FG cylindrical shell are discussed, and an analytical method for predicting elastic buckling pressure is presented based on the relationship between the natural frequency and internal pressure.更多还原