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中文摘要：
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。
英文摘要：
Abstract= Based on the two-parameter foundation model of horizontal shear deformation and vertical com- pressive deformation, the deflection equation of rectangular plate on viscoelastic foundation under the ac- tion of load using fractional derivatives was established. According to the correspondence principle of elas- ticity and viscoelasticity and Laplace transform, the elastic solution of rectangular plate with four edges simply supported was extended to the cooresponding problrm of plate on the fractional derivative viscoe- lastic foundation. The example indicated that the fractional derivative viscoelastic model was more adap- tive than the classical viscoelastic model, and also the influence of the model parameters on the deflection- time relationship was analyzed.
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