移动荷载作用下横观各向同性层状地基–薄板结构动力响应半解析研究
Semi-analytical solution to dynamic response of transversely isotropic layered foundation-thin plate structure under moving loads
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摘要: 为研究各向异性和动载参数对层状地基–薄板结构动力响应的影响规律,在已有各向异性弹性动力学理论的基础上,利用积分变换及矩阵分析理论,获得移动矩形简谐荷载作用下横观各向同性层状地基–薄板(无限大)结构的稳态动力响应半解析解答。通过对比既有算例所得结果,验证半解析解的准确性,进而对板体位移动力响应进行参数分析。结果表明:各向同性、横观各向同性假设下的计算结果存在较大差异。移动荷载较静载使板体位移幅值不对称分布,且存在临界速度使荷载作用区域幅值最大。荷载激振频率增大会减小板体竖向位移的响应范围。第一层地基的各向异性水平相较其余层对板体位移影响较大,增大其n值(水平、竖直弹性模量比)可改善板体在动力作用下的位移响应分布特征。Abstract: To study the influences of anisotropy and dynamic parameters on the response of a layered foundation-thin plate structure, from the basis of the anisotropic elastodynamics, a semi-analytical solution to the dynamic response of TI layered foundation-thin plate (infinite) model under moving rectangular harmonic loads is established by using the integral transformation and the matrix theory. The accuracy of the semi-analytical solution is verified by comparing the results of the existing examples, and then the parametric analysis of the displacement dynamic response of the plate is carried out. The results show that there is a large difference between the calculated results under the assumption of isotropy and transverse isotropy. Compared with that of the static loads, the displacement amplitude of the moving loads is asymmetric, and there is a critical velocity which makes the maximum amplitude of the loading area. The affected range of the displacement reduces with the increase of the frequency. The anisotropy of the first layer has a greater impact on the displacement than other layers. Adjusting its n value can optimize the displacement characteristics of the plate under dynamic loads.