【摘要】 研究了具有指数型体积分数的功能梯度材料圆柱壳自由振动的固有频率。根据Love薄壳理论,确定功能梯度材料圆柱壳的内力、位移、应变和曲率的关系式;利用Rayleigh-Ritz方法建立了功能梯度材料圆柱壳自由振动固有频率的特征方程,推导出一端固定一端自由、两端简支两种基本边界条件下的固有频率参数表达式。最后通过两类材料组分的算例,分析了材料组分、体积分数、边界条件以及几何尺寸等因素对功能梯度材料圆柱壳的固有频率的影响。研究表明,构成功能梯度材料的材料组分对FG圆柱壳的频率特征有着明显的影响,体积分数所产生的影响则相对有限;而不同边界条件对FG圆柱壳固有频率的影响主要表现在壳体长度与半径比较小和周向波数较小的情况下。更多还原

【Abstract】 The vibration of cylindrical shells composed of functionally graded material and with exponential volume fraction law is studied.Expressions of the internal force,displacement,strain and curvature of FG cylindrical shells are analysed by Love’s thin shell theory.Based on the Rayleigh-Ritz method,the shell eigenfrequency equation is derived and the natural frequencies with simply supported ends and clamped-free ends are obtained.Then the influence of the configurations of constituent materials,volume fraction,boundary conditions and geometric dimensioning on the natural frequencies of FG cylindrical shells is studied through the examples.The results show that the configurations of constituent materials have considerable effect on the frequency characteristic of FG cylindrical shells,while the volume fraction has minor effect.The influence of various boundary conditions on natural frequencies is mainly reflected in the cases of small ratios of length to radius and small circumferential wave numbers.更多还原