發(fā)布時(shí)間：2018-08-14 17:10

【摘要】：基于彈性地基Pasternak雙參數(shù)模型,利用分?jǐn)?shù)階微分得到黏彈性地基雙參數(shù)模型,并在此基礎(chǔ)上建立采用分?jǐn)?shù)階微分Kelvin模型的雙參數(shù)黏彈性地基上彈性和黏彈性矩形板在動(dòng)荷載作用下的動(dòng)力方程;利用Galerkin方法和分段處理的數(shù)值計(jì)算方法求解四邊簡(jiǎn)支的彈性和黏彈性地基板的動(dòng)力方程,通過(guò)自由振動(dòng)算例驗(yàn)證該求解方法的正確性;并分析沖擊動(dòng)荷載作用下分?jǐn)?shù)階微分Kelvin模型的分?jǐn)?shù)階、粘滯系數(shù)、水平剪切系數(shù)和模量參數(shù)對(duì)位移響應(yīng)的影響。結(jié)果表明:分?jǐn)?shù)階微分黏彈性模型可以描述不同黏彈性材料的力學(xué)行為;分?jǐn)?shù)階取值0.5前后,矩形板位移響應(yīng)值出現(xiàn)了不同的衰減發(fā)展形態(tài);粘滯系數(shù)、水平剪切系數(shù)和模量系數(shù)取值越大,位移響應(yīng)衰減速度越快。
[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.
【作者單位】： 同濟(jì)大學(xué)地下與建筑工程系;
【基金】：教育部長(zhǎng)江學(xué)者和創(chuàng)新團(tuán)隊(duì)發(fā)展計(jì)劃(IRT1029)
【分類號(hào)】：TU470

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