【摘要】：研究了黏彈性地基上變厚度矩形薄板的動(dòng)力響應(yīng)。采用分?jǐn)?shù)階微分的Kelvin-voigt模型描述地基的黏彈性特征,基于彈性板的基本假設(shè),對(duì)于小變形問(wèn)題,建立了黏彈性地基上變厚度矩形薄板的動(dòng)力控制微分方程。針對(duì)該分?jǐn)?shù)階變系數(shù)偏微分方程,采用Galerkin法和Haar小波配點(diǎn)法進(jìn)行數(shù)值求解。分析了四邊簡(jiǎn)支板的動(dòng)力響應(yīng)特性,得到了均布載荷作用下線性模型、拋物線模型板中心撓度曲線,討論了變厚度矩形板的厚度比、長(zhǎng)寬比、分?jǐn)?shù)階導(dǎo)數(shù)的階數(shù)、地基彈簧系數(shù)、粘滯系數(shù)、水平剪切系數(shù)等參數(shù)變化對(duì)板動(dòng)力特性的影響。
[Abstract]:The dynamic response of rectangular thin plates with variable thickness on viscoelastic foundation is studied. The fractional differential Kelvin-voigt model is used to describe the viscoelastic characteristics of the foundation. Based on the basic assumptions of elastic plates, the dynamic governing differential equations of rectangular thin plates with varying thickness on viscoelastic foundations are established for small deformation problems. Galerkin method and Haar wavelet collocation method are used to solve the fractional variable coefficient partial differential equation. In this paper, the dynamic response characteristics of simply supported plates with four edges are analyzed. The linear model and the central deflection curve of parabola model under uniform load are obtained. The thickness ratio, aspect ratio and order of fractional derivative of rectangular plates with variable thickness are discussed. The influence of spring coefficient, viscosity coefficient and horizontal shear coefficient on the dynamic characteristics of plate.
【作者單位】： 西安理工大學(xué)理學(xué)院;
【基金】：陜西省自然科學(xué)資金項(xiàng)目(2011JM1013) 陜西科學(xué)技術(shù)攻關(guān)項(xiàng)目(2015GY004)資助
【分類號(hào)】：O341

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