弹性地基中含孔隙的功能梯度圆锥壳的振动分析

VIBRATION ANALYSIS OF FUNCTIONALLY GRADED POROUS CONICAL SHELLS RESTED ON ELASTIC FOUNDATIONS

为研究弹性地基中多孔功能梯度材料圆锥壳的振动特性,基于经典薄壳理论建立了弹性地基中含均匀和非均匀分布孔隙的功能梯度材料圆锥薄壳的振动方程,并用伽辽金法求得了自由振动和动力响应的解。通过参数分析讨论了孔隙、弹性地基参数、半锥角等因素对功能梯度圆锥壳自由振动和动力响应的影响。结果表明,弹性地基的压缩和剪切刚度的增大提高了圆锥壳的振动频率而显著减小了动力响应;当半锥角增大时,圆锥壳的动力响应显著增大。与非均匀分布孔隙壳体相比,均匀分布孔隙壳体的自振频率和动力响应随孔隙率的变化更为敏感。

To study the vibration characteristics of porous functionally graded conical shells on elastic foundations, the vibration equations for the functionally graded conical shells with evenly and unevenly distributed pores are derived based on the classical shell theory. The solutions of the free vibrations and the dynamic responses for the shells are obtained by using the Galerkin method. The effects of pores, elastic foundation parameters, semi-vertex angle and other factors on the natural frequencies and the dynamic responses are investigated. The results show that the natural frequencies rise with the increase of the elastic foundation parameters.However, the dynamic responses are significantly reduced. The results also demonstrate that the dynamic responses are increased significantly by increasing semi-vertex angle. Compared with unevenly distributed pores,the effects of evenly distributed pores on the natural frequencies and the dynamic responses are more evident.