第一类算子方程的吉洪诺夫正则解的收敛性和渐近阶估计

本文对于第一类算子方程当右端近似给定和当算子与右端皆近似分别给定时,讨论如何确定正则参数。并给出吉洪诺夫正则解的收敛性和渐近阶估计。     

Numerical algorithm for the dynamic analysis of base-isolated structures with dry friction

This paper deals with the techniques for solving ordinary differential equations with essential nonlinearity arising from the representation of frictional force by the sign function of the relative velocity. This problem is connected with dynamic behavior studies of base-isolated structures with dry friction devices.Mathematical evidence is presented concerning the inaccuracies of the solution which are connected with the representation of the frictional force by the sign function. An approximation of this sign model is made on the basis of the appropriate linearization of a small part of the frictional force function. A numerical algorithm for the dynamic analysis of base-isolated structures with dry friction is proposed. Numerical tests are carried out for establishing the exactness of the proposed techniques. The obtained results prove the accuracy of the techniques.     

Applications of seismic moment tensor inversion in fast response to earthquakes

IntroductionAfteramoderateorstronger(Ms25.0)earthquake,themosturgentworkofthedivisionforearthquakemonitoringandpredictionistodetermineitstimeoforigin,hypocentrallocation(longitude,latitudeanddepth)andmagnitudeandtojudgethetrendofseismicregimedevelopmentassoonaspossible.Ingeneralcases,whenanearthquakewithMS25.0insideChinaoraonewithMS26.0inneighboringareasofChinahasoccurred,theEarthquakeBulletinofChineseSeismologicalNetworkcanprovidedeterminationoftheorigintime,hypocentrallocation(longitude,…     

The gravitational perturbation spectrum in linear satellite theory

A new method for calculating the perturbation spectrum in the framework of Kaula's linear satellite theory (LST) is introduced. The novelty of this approach consists in using recent results on the spectral decomposition of the perturbation frequencies in LST to provide a closed formulation for the amplitude and the phase of each line in the perturbation spectrum. The theory presented here can be applied to perturbations in the elements or in the radial and transverse directions due to the geopotential or to the tides. Separate algorithms are developed for application to orbits with circulating or frozen perigee.     

Diffusive wave solutions for open channel flows with uniform and concentrated lateral inflow

The diffusive wave equation with inhomogeneous terms representing hydraulics with uniform or concentrated lateral inflow into a river is theoretically investigated in the current paper. All the solutions have been systematically expressed in a unified form in terms of response function or so called K-function. The integration of K-function obtained by using Laplace transform becomes S-function, which is examined in detail to improve the understanding of flood routing characters. The backwater effects usually resulting in the discharge reductions and water surface elevations upstream due to both the downstream boundary and lateral inflow are analyzed. With a pulse discharge in upstream boundary inflow, downstream boundary outflow and lateral inflow respectively, hydrographs of a channel are routed by using the S-functions. Moreover, the comparisons of hydrographs in infinite, semi-infinite and finite channels are pursued to exhibit the different backwater effects due to a concentrated lateral inflow for various channel types.     

Yielding oscillator subjected to simple pulse waveforms: numerical analysis & closed‐form solutions

Numerical and analytical solutions are presented for the elastic and inelastic response of single‐degree‐of‐freedom yielding oscillators to idealized ground acceleration pulses. These motions are typical of near‐fault earthquake recordings generated by forward rupture directivity and may inflict damage in the absence of substantial structural strength and ductility capacity. Four basic pulse waveforms are examined: (1) triangular; (2) sinusoidal; (3) exponential; and (4) rectangular. In the first part of the article, a numerical study is presented of the effect of oscillator period, strength, damping, post‐yielding stiffness and number of excitation cycles, on inelastic response. Results are presented in the form of dimensionless graphs and regression formulas that elucidate the salient features of the problem. It is shown that conventional R–µ relations may significantly underestimate ductility demand imposed by near‐fault motions. The second part of the article concentrates on elastic‐perfectly plastic oscillators. Closed‐form solutions are derived for post‐yielding response and associated ductility demand. It is shown that all three ground motion histories (i.e. acceleration, velocity, and displacement) control oscillator response—contrary to the widespread view that ground velocity alone is of leading importance. The derived solutions provide insight on the physics of inelastic response, which is often obscured by the complexity of numerical algorithms and actual earthquake motions. The model is evaluated against numerical results from near‐field recordings. A case study is presented. Copyright © 2006 John Wiley & Sons, Ltd.     

进化策略算法在地面沉降量计算参数反演中的应用

多数情况下,评估的研究区缺乏多年积累的地下水位及开采量资料。因此,通常采用土力学模型,根据太沙基固结理论,进行地面沉降量预测。在地面沉降量计算中,土层变形参数值的选取直接影响计算结果的精确性。深层含水层埋深通常大于100m。通过现场勘探,采取土样进行岩土物理力学性质试验获取参数值,成本过于昂贵。通过参考区域土层物理力学性质资料,结合工程经验获取参数值,预测结果的精度得不到保证。针对上述情况,作者提出用非线性优化算法-进化策略算法,根据实测地面沉降量反演土层变形参数值。通过这种方法确定参数值,既节约成本,又保证了计算结果的可靠性。进化策略算法通过模拟生物遗传及进化过程,利用转移概率来帮助指导搜索。搜索结果不依赖于初始点的选择,对于求解全局最优解有很强的鲁棒性。作者将进化策略算法用于某一工程实例土层变形参数的反演,结果表明了该算法的可行性及稳健性,值得在工程实践中推广应用。