粘弹性地基上含孔隙的石墨烯增强功能梯度板的振动

为分析粘弹性地基上含孔隙的石墨烯增强功能梯度板的自由和强迫振动特性，基于三参数粘弹性地基模型及复合材料薄板理论，建立了粘弹性地基上含孔隙石墨烯增强功能梯度板的运动方程，用伽辽金法求解其固有频率和动力响应，并通过数值算例分析了粘弹性地基参数、孔隙率、孔隙类型及石墨烯纳米片分布模式、含量等因素对自由振动和动力响应的影响．结果表明，固有频率随着孔隙率的增大非单调变化，孔隙率对固有频率的影响随着地基参数、孔隙类型的不同而不同．另外，在三种孔隙类型中，上下表面层含有最少孔隙数量的板的动挠度最小，且其动挠度随着孔隙率的增大而微弱提高．

On the Vibration of Functionally Graded Graphene-Reinforced Porous Plates on Viscoelastic Foundations

The present paper analyzes the vibrational characteristics of the functionally graded graphene-reinforced porous plates on viscoelastic foundations. Based on the three-parameter model of viscoelastic foundation and the composite thin plate theory, the equations of motion for functionally graded graphene-reinforced porous plates on viscoelastic foundations are established. Galerkin method is used to solve the free vibrations and the dynamic responses of the plates. The numerical examples are used to analyze the influences of the foundation parameters, the porosity coefficients, the porosity distributions, the distribution patterns and the weight fraction of graphene nanoplatelets on the natural frequencies and dynamic responses. The results show that the natural frequencies change non-monotonically with the increase of porosity coefficients, and the effect of porosity coefficients on the natural frequencies vary with different foundation parameters and porosity distributions. Among the three porosity distributions, the central transient deflections of the plates are the smallest for the case with minimum number of pores on the top and bottom surfaces, and increase slightly with the increase of porosity coefficients.