分数阶微分双参数黏弹性地基矩形板动力响应

基于弹性地基Pasternak双参数模型，利用分数阶微分得到黏弹性地基双参数模型，并在此基础上建立采用分数阶微分Kelvin模型的双参数黏弹性地基上弹性和黏弹性矩形板在动荷载作用下的动力方程；利用Galerkin方法和分段处理的数值计算方法求解四边简支的弹性和黏弹性地基板的动力方程，通过自由振动算例验证该求解方法的正确性；并分析冲击动荷载作用下分数阶微分Kelvin模型的分数阶、粘滞系数、水平剪切系数和模量参数对位移响应的影响。结果表明：分数阶微分黏弹性模型可以描述不同黏弹性材料的力学行为；分数阶取值0.5前后，矩形板位移响应值出现了不同的衰减发展形态；粘滞系数、水平剪切系数和模量系数取值越大，位移响应衰减速度越快。

Dynamic response of rectangular plate on two-parameter viscoelastic foundation with fractional derivative

Based on the two-parameter Pasternak model of elastic foundation, the two-parameter model of viscoelastic foundation was derived by using fractional derivative. The equation of elastic and viscoelastic rectangular plate under the dynamic load on two-parameter viscoelastic foundation with the fractional Kelvin model was established. The equation of elastic and viscoelastic rectangular plate with four edges simply supported was solved by the Galerkin method and the segmented numerical method, the correctness of the solution was verified by the example of free vibration. The influences of the fractional order, viscosity parameter, horizontal shear parameter and modulus parameter on the displacement of the fractional Kelvin model with impact load were analyzed. The results show that the fractional derivative viscoelastic model may describe the mechanical behavior of different viscoelastic materials; the displacement response of rectangular plate appears different attenuation formation before and after the fractional order value of 0.5; the attenuation speed of the displacement response increases with the increasing of the viscosity parameter, horizontal shear parameter and modulus parameter.