弹簧地基上大直径单桩海上风机的一阶自振频率

自振频率是海上风机前期动力设计的主要难点之一,计算精度要求极高,而桩-土相互作用对自振频率影响显著。目前,针对桩-土相互作用普遍采用弹簧地基简化模型,为对比分析不同弹簧地基简化模型的准确性和精度,本文采用回传射线矩阵法,建立固定端、单弹簧、双弹簧和三弹簧这4种地基简化模型,基于Bernoulli-Euler梁理论和Timoshenko梁理论,求解风机系统的自振频率,并与风机基频实测值作对比,进一步分析三弹簧简化地基模型中地基旋转刚度、地基耦合刚度和地基水平刚度对风机系统基频的影响。研究结果表明,桩-土相互作用不可忽略,三弹簧地基简化模型计算风机系统基频精度最高;地基刚度对风机系统基频的敏感性次序为,地基耦合刚度>地基旋转刚度>地基水平刚度;当地基旋转(水平)刚度较小时,地基耦合刚度与地基旋转(水平)刚度的耦合效应对风机系统的基频影响较大;地基耦合刚度与地基旋转刚度的耦合效应对风机系统基频的影响程度大于地基耦合刚度与地基水平刚度的耦合效应。     

The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadings

Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth‐order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r → 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz‐type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory

The main objective of this research work is to present analytical solutions for free vibration analysis of moderately thick rectangular plates, which are composed of functionally graded materials (FGMs) and supported by either Winkler or Pasternak elastic foundations. The proposed rectangular plates have two opposite edges simply-supported, while all possible combinations of free, simply-supported and clamped boundary conditions are applied to the other two edges. In order to capture fundamental frequencies of the functionally graded (FG) rectangular plates resting on elastic foundation, the analysis procedure is based on the first-order shear deformation plate theory (FSDT) to derive and solve exactly the equations of motion. The mechanical properties of the FG plates are assumed to vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. First, a new formula for the shear correction factors, used in the Mindlin plate theory, is obtained for FG plates. Then the excellent accuracy of the present analytical solutions is confirmed by making some comparisons of the results with those available in literature. The effect of foundation stiffness parameters on the free vibration of the FG plates, constrained by different combinations of classical boundary conditions, is also presented for various values of aspect ratios, gradient indices, and thickness to length ratios.     

用改进的传输线算法计算水平层状横向同性地层中海洋可控源电磁响应

利用二维Fourier变换与电磁场分解技术将层状横向同性地层中Maxwell方程转化成两个独立的关于横磁(TM)波和横电(TE)波的传输线方程; 借助传输线理论与叠加原理, 仅利用电流源传输线Green函数得到TM波和TE波的解, 改进传输线算法, 建立横向同性地层中频率-波数域电流源电场和磁场并矢Green函数的新算法与新的解析表达式, 提高海洋可控源电磁响应数值模拟效率. 在此基础上, 利用传输线Green函数的基本解以及边界条件, 推导出广义反射系数与振幅递推公式, 得到各个地层中传输线Green函数的解析解; 然后利用Fourier逆变换与Bessel公式将海洋可控源电磁响应表示为Sommerfeld形式的积分, 借助三次样条插值与Lommel积分公式快速计算其数值解. 通过数值模拟结果考察工作频率以及地层各向异性电阻率变化等对海洋电磁响应的影响. 关键词： 传输线法 横向同性地层 海洋可控源电磁 Sommerfeld积分