考虑横向拉伸的FGM夹层双曲扁壳自由振动分析

Free vibration of functionally graded material sandwich double curved shallow shells with stretching effects

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。

Free vibration of functionally graded material(FGM) sandwich double curved shallow shells based on an improved hyperbolic sine shear deformation theory with stretching effects is presented. The dynamic model is obtained by the Hamilton principle. The dimensionless natural frequencies with FGM face sheet and homogeneous core under simply supported conditions are calculated by Navier method and compared with the results from the classical laminated theory, the first-order shear deformation theory, hyperbolic sinusoidal shear deformation theory and other previous research obtained results. Effects of gradient parameter, core thickness and length-thickness ratio on frequency are analyzed. Numerical experiments show that the results based on the new higher order shear deformation theory in this paper are more accurate than others. The dimensionless natural frequency of FGM sandwich double curved shallow shells decreases with the increase of gradient material properties change index, increases monotonically with the thickness of the core layer and the length-thickness ratios.