分数阶微分双参数黏弹性地基矩形板动力响应

发布时间：2018-08-14 17:10

【摘要】：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。
[Abstract]:Based on the Pasternak two-parameter model of elastic foundation, the two-parameter model of viscoelastic foundation is obtained by fractional differential. On this basis, the dynamic equations of elastic and viscoelastic rectangular plates on a two-parameter viscoelastic foundation with fractional differential Kelvin model under dynamic load are established. The Galerkin method and the piecewise numerical method are used to solve the dynamic equations of elastic and viscoelastic foundation plates with simply supported four sides. The correctness of the method is verified by a free vibration example. The effects of fractional order, viscosity coefficient, horizontal shear coefficient and modulus parameters on displacement response of fractional differential Kelvin model under impact dynamic loading are analyzed. The results show that the fractional differential viscoelastic model can describe the mechanical behavior of different viscoelastic materials, the displacement response values of rectangular plates appear different decay development forms before and after the fractional order value 0.5, and the viscosity coefficient, The larger the horizontal shear coefficient and modulus coefficient, the faster the attenuation rate of displacement response.
【作者单位】：同济大学地下与建筑工程系;
【基金】：教育部长江学者和创新团队发展计划(IRT1029)
【分类号】：TU470

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