黏弹性地基上功能梯度材料板的振动分析

为研究黏弹性地基上功能梯度材料板的自由和强迫振动特性,基于Reddy高阶剪切变形理论以及由Shen导得的广义Karman型方程,用双重Fourier级数法推导了三参数黏弹性地基上四边简支功能梯度材料板自由振动和动力响应的解析解,计算了各模态自振频率和半波冲击载荷作用下的动力响应,讨论了材料组分指数、黏弹性地基参数、边厚比等因素对自由振动和动力响应的影响.结果表明,黏弹性地基的剪切和压缩刚度显著提升了功能梯度材料板的振动频率,减小了动力响应;另外,地基的黏性对振动频率和动力响应也有一定的影响.

THE VIBRATION OF FUNCTIONALLY GRADED PLATES RESTING ON VISCOELASTIC FOUNDATIONS

The present paper analyzes the vibration of simply supported plates of functionally graded materials resting on viscoelastic foundations. Based on the Reddy's higher-order shear deformable plate theory and the general Karman-type equations derived by Shen, the analytical solutions for the free vibration and the transient response are obtained by using the double Fourier series. The natural frequencies and the transient response are obtained, and the results are compared with those of other papers. The effects of the volume fraction index, the parameters of the viscoelastic foundations and the ratio of the length to the thickness are analyzed. The results show that the natural frequencies rise, but the transient responses decrease with the increase of the pressed and sheared parameters of the viscoelastic foundations, and the viscous parameter also has an effect on the natural frequencies and the transient response.