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基于考虑水平剪切变形和竖向压缩变形的双参数地基模型,利用分数阶微分建立了黏弹性地基上矩形薄板荷载作用下的挠度方程;根据弹性-黏弹性对应原理,通过Laplace变换将四边简支矩形板弹性问题的解推广求解分数阶微分黏弹性问题;通过算例表明分数阶微分型黏弹性模型比经典黏弹性模型的适应性,并分析了模型参数对挠度-时间关系的影响。
Based on the two-parameter foundation model considering the horizontal shear deformation and the vertical compression deformation, the deflection equation of the thin plate under viscoelastic foundation is established by using the fractional differential method. According to the principle of elasticity-viscoelasticity, The solution to the problem of fractional differential viscoelasticity is solved by the solution of the elastic problem of the support rectangular plate. The example shows the adaptability of the fractional differential viscoelastic model to the classical viscoelastic model and the influence of the model parameters on the deflection-time relationship.