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在双曲正弦高阶剪切变形理论的基础上,针对横向位移增加厚度坐标的幂函数项,考虑了横向拉伸的影响,研究了简支条件下功能梯度夹层双曲扁壳的自由振动。基于Hamilton原理推导出了其动力学模型,利用Navier方法计算了表层是功能梯度材料,芯层是匀质材料的双曲扁壳的量纲为一的固有频率,并与已有结果进行了比较。分析了功能梯度材料性质梯度变化指数、芯层厚度、长厚比、曲率半径与厚度比对量纲为一的固有频率的影响。结果表明:与已有结果比较,基于考虑横向拉伸影响的正弦剪切变形理论,功能梯度夹层双曲扁壳对量纲为一的固有频率的计算结果是准确的;量纲为一的固有频率随着材料性质梯度变化指数的增加而单调减小,随着长厚比的增加而单调增加,随着芯层厚度的增加而单调增加。
Based on hyperbolic sine high-order shear deformation theory, considering the influence of transverse stretching on the power function term of increasing thickness coordinate of lateral displacement, the free vibration of functionally graded double-layered shallow shells under simple support condition is studied. Based on the principle of Hamilton, the kinetic model is deduced. The Navier method is used to calculate the natural frequency of the hyperbolic flat shell whose surface is a functionally graded material and whose core is a homogenous material, and compared with the existing results . The influence of graded index, core thickness, aspect ratio, radius of curvature and thickness ratio on the natural frequency of one dimension of functional graded material was analyzed. The results show that, compared with the previous results, the calculated results of the natural frequencies of one dimension are accurate based on the sinusoidal shear deformation theory which considers the effect of transverse tension. The frequency decreases monotonously with the increase of gradient index of material property, monotonically increases with the increase of aspect ratio, and monotonically increases with the increase of core thickness.