高拱坝气幕隔震的动力模型试验

为了研究高拱坝的气幕隔震效果,基于动力相似准则,设计了坝体-坝基-气幕-库水三相耦合系统的动力试验模型。其中,坝体材料采用河沙、重晶石粉、铁粉、松香、酒精调制而成,坝基材料采用膨胀珍珠岩和石膏调制的轻质材料,气幕厚度为1cm,均匀地覆盖在坝体上游面,气室壁材料选用ABS工程塑料。基于该模型,完成了两种实测地震波不同峰值加速度共计12个工况的大型振动台试验。试验结果表明:气幕使动水压力显著降低,坝体加速度也相应减小;靠近坝底的测点动水压力削减达70%以上,坝顶加速度减小约20%。因此,气幕可提高坝体的抗震性能。     

地震作用下高拱坝损伤开裂分析

采用应变率相关的砼非线性损伤模型模拟拱坝横缝,研究了砼非线性本构情况下整体拱坝与考虑分缝拱坝的应力响应和损伤开裂的特点与差别。对实际拱坝的地震响应分析表明,基于非线性砼模型的整体拱坝动力响应模型可以基本反映拱坝的实际应力分布情况。     

非线性子结构方法中实现对结构抗震措施阻尼器的数值模拟

应用子结构理论,对设置伸缩横缝的小湾高拱坝结构,分别就正常高水位常遇低水位两种水位工况,考虑坝体伸缩横缝在地震交变荷载作用下反复开合引起的缝面问滑移．接触等效应的影响,坝体一库水的相互作用而产生的动水压力的影响,对坝体的抗震性能进行了地震反应分析。对伸缩缝问设置阻尼器这一新的设计思想进行了可行性的研究,论证推导了阻尼器的计算模型,探讨了阻尼器对坝体结构抗震性能的影响。     

高拱坝动力特性与动力响应模型试验研究

高拱坝的动力破坏特性越来越受到关注,动力特性和动力响应是其研究的一个重要方面。通过模型试验的方法研究高拱坝动力特性和动力响应的特征,动力特性试验比较了完好结构与有施工横缝结构的基阶动力特性,表明当结构存在施工横缝时,结构基阶频率降低,阻尼增大。结构动力响应采用振动台模拟地震波激励,试验结果表明,完整结构与有施工缝结构动力响应具体数据不同,但规律相同。加速度最大响应沿拱顶水平向在坝中拱顶的值最大,向两边的坝肩处,加速度最大响应逐渐减小。沿拱坝垂向加速度最大响应从坝顶到基础,响应均逐渐减小。试验结果可为高拱坝结构动力安全研究提供技术依据。     

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.     

考虑局部切向约束接触问题的直接刚度法

针对工程中大量存在的切向滑移受到约束的接触问题,提出了基于Lagrange乘子的点-面及点-点接触直接刚度法,该方法生成的接触协调条件可以直接组装到结构刚度阵中,从而可直接用于考虑存在结构几何非线性及材料非线性的接触问题分析中。采用这一算法进行了考虑拱坝横缝张合效应的地震响应分析,结果表明考虑切向滑移约束对接触中的张开度有明显影响。     

Reservoir water level effects on nonlinear dynamic response of arch dams

In this study, reservoir water level effects on nonlinear dynamic response of arch dams are investigated. For this purpose, the nonlinear behaviour of the dam concrete is idealized as elasto-plastic using the Drucker–Prager model based on the associated flow rule assumption. Water in the reservoir is represented by the Lagrangian (displacement-based) fluid finite elements. The program NONSAP is modified for elasto-plastic analysis of fluid–structure systems and employed in the response calculations. Nonlinear dynamic analysis of an arch dam subjected to earthquake ground motion is performed for five different water levels. The El-Centro N–S component of the Imperial Valley earthquake, on May 18, 1940, has been used as the ground motion. The crest displacements, the maximum tensile stresses on the upstream and downstream faces of the dam and the time history of the yield function of an element in the dam body are presented. The results obtained from nonlinear analyses for different water levels are compared with each other. It is apparent that the reservoir water level effects must be considered in the elasto-plastic analyses of arch dams to earthquake ground motion.     

A comparison of two formulations of the fin efficiency for straight fins

A formulation of the fin efficiency based on Newton’s law of cooling is compared with a formulation based on a ratio of heat transferred from the fin surface to the surrounding fluid to the heat conducted through the base.The first formulation requires that the solution of the nonlinear fin equations for constant heat transfer coefficient and constant thermal conductivity is known,whilst the second formulation of the fin efficiency requires only that a first integral of the model equation is known.This paper shows the first formulation of the fin efficiency contains approximation errors as only power series and approximate solutions to the nonlinear fin equations have been determined.The second formulation of the fin efficiency is exact when the first integrals can be determined.     

考虑混凝土应变率变化的高拱坝非线性动力响应研究

提出一种新的应变率相关的混凝土非线性弹塑性损伤模型。采用此模型对混凝土拱坝的非线性地震响应作了分析。在综合考虑坝-地基-库水动力相互作用和坝缝非线性接触的基础上，着重研究了混凝土应交率相关效应及加载历史对混凝土极限强度等重要参数及拱坝响应的影响，并与采用不考虑应交率影响的混凝土损伤模型计算结果进行了对比分析。结果表明，拱坝考虑横缝作用后的坝面应变率分布不同于整体拱坝。应交率分布形态不仅可以很好地表征拱坝的振动形态，而且对于高拱坝的动力响应的影响也不可忽略。     

Regional plantar foot pressure distributions on high-heeled shoes-shank curve effects

Forefoot pain is common in high-heeled shoe wearers due to the high pressure caused by the center of body mass moving forward and the increased arch height with heel elevation.Sufficient arch support could reduce the high pressure over forefoot.However,too much arch support could lead to abnormal foot alignment and pain over midfoot.Little information is reported on the relationship among plantar arch height,shank curve design and plantar pressure.This study aimed at quantifying the plantar arch height changes at different heel heights and investigating the effect of shank curve on plantar pressure distribution.The plantar arch height increased to(7.6±1.3) mm at heel height of 75 mm.The Chinese standard suggests the depth of last should be 8.5 mm for heel height of 75 mm.When a shank curve with higher depth of last(11 mm) was used,the peak pressure over forefoot further decreased in midstance phase,which might ease the forefoot problems,while the peak pressure over midfoot increased but not exceeded the discomfort pressure thresholds.To achieve a more ideal pressure distribution in high-heeled shoes,a higher than expected depth of last would be suggested that would not cause discomfort over midfoot.     

高拱坝伸缩横缝间布设抗震钢筋的动力反应分析

应用动力非线性子结构理论,对设置伸缩横缝的小湾高拱坝实际工程结构抗震分析中的坝体横缝加抗震钢筋问题进行了研究。讨论并建立了坝体伸缩横缝在地震荷载作用下穿越缝间抗震钢筋的数学模型,给出了动力非线性子结构法考虑缝间抗震钢筋影响的求解公式;并就正常高水位常与低水位两种水位工况,对坝体的抗震性能进行了计算分析。讨论了在地震荷载作用下抗震钢筋对坝体横缝张开度、坝体应力以及加速度响应的影响。     

Dynamic Characteristics of a Prototype Arch Dam

This study determines the dynamic characteristics of a prototype arch dam-reservoir-foundation system using Operational Modal Analysis method. Achievement of this purpose involved construction of a prototype arch dam-reservoir-foundation system under laboratory conditions. Ambient vibration tests on the arch dam model identified its natural frequencies, mode shapes, and damping ratios. Natural excitations such as small impact loads vibrated to arch dam. Sensitivity accelerometers which were placed on the dam’s crest collected signals in measurements. Measurements were recorded for empty and full reservoirs. Operational Modal Analysis software processed signals which were collected from the ambient vibration tests. Enhanced Frequency Domain Decomposition technique estimated dynamic characteristics of the dam. Results showed that there was an approximate 20–25% difference between natural frequencies related to empty and full reservoirs.     

An investigation of an Emden-Fowler equation from thin film flow

A third-order ordinary differential equation (ODE) for thin film flow with both Neumann and Dirichlet boundary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions.Numerical solutions of the nonlinear second-order ODE are investigated using finite difference schemes.A finite difference formulation to an Emden-Fowler representation of the second-order nonlinear ODE is shown to converge faster than a finite difference formulation of the standard form of the second-order nonlinear ODE.Both finite difference schemes satisfy the von Neumann stability criteria.When mapping the numerical solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line.A nonlinear relationship between the position of the contact line and physical parameters is obtained.     

含缝拱坝强震失效破坏振动台试验研究

为探究强震时含缝拱坝结构的承载能力及失效路径,在振动台上开展了一系列拱坝模型强震失效破坏试验。基于弹性力-重力准则设计试验,分别进行了不分缝、只有横缝、诱导缝与横缝联合作用这三种情况的振动台模型试验,试验中考虑了材料率相关性的影响,忽略了库水-拱坝相互作用。结果表明,强震作用时由于设缝处的抗拉能力较低,导致缝位置首先发生开裂,拱向应力的传导路径遭到破坏,此后结构破坏以悬臂梁形式为主;科学合理设置缝的形式和位置,可以有效耗散地震能量,提高拱坝极限承载能力。本文研究结果可为高拱坝的抗震分缝设计和超载能力评估提供试验依据。     

On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

Dynamic analysis of an offshore pipe laying operation using the reel method

A system designed for a rigid and flexible pipe laying purposes is presented in the paper.Mathematical and numerical models are developed by using the rigid finite element method(RFEM).The RFEM is an efficient solution in the time domain.Static and dynamic problems related to pipe installation are solved by taking the advantage of simple interpretation and implementation of the method.Large deformations of the pipe during spooling and when it is reeled out at sea are considered.A material model implemented is used to take into consideration nonlinear material properties.In particular,the full elasto-plastic material characteristics with hardening and Bauschinger effect are included.Dynamic analyses are performed and the results attached in this work demonstrates how the sea conditions influence the machinery and pipeline,assuming a passive reel drive system. The influence of several other operational parameters on dynamic loads is verified.An active system,implemented as a part of the mathematical model,improves the system performance.Some results are presented as well.     

Comparison of near- and far-fault ground motion effect on the nonlinear response of dam–reservoir–foundation systems

In this paper, it is aimed to compare the near- and far-fault ground motion effects on the nonlinear dynamic response of dams including dam–reservoir–foundation interaction. Two different types of dams, which are concrete arch and concrete faced rockfill dams, are selected to investigate the near- and far-fault ground motion effects on the dam responses. The behavior of reservoir water is taken into account using Lagrangian approach. The Drucker–Prager material model is employed in nonlinear analyses. Near and far-fault strong ground motion records, which have approximately identical peak ground accelerations, of Loma Prieta (1989) earthquake are selected for the analyses. Displacements, maximum and minimum principal stresses are determined using the finite element method. The displacements and principal stresses obtained from the analyses of dams subjected to each fault effect are compared with each other. It is clearly seen that there is more seismic demand on displacements and stresses when the dam is subjected to near-fault ground motion.     

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

This paper develops a coupled dynamics model for a linear induction motor (LIM) vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen- Hedrick-Elkins’ model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system (LMS), Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.     

Coupling dynamic analysis of a liquid-filled spherical container subject to arbitrary excitation

Using spherical coordinates, the coupling nonlin- ear dynamic system of a liquid-filled spherical tank, which can be excited discretionarily, is deduced by the H-O variational principle, and the viscous damping is introduced via the liquid dissipation function. The kinetic equations of the coupling system are deduced by the relationship between the velocity of liquid particles and the disturbed liquid surface equation. Normal differential equations are obtained through the Galerkin method. An equivalent mechanical model is developed for liquid sloshing in a spherical tank subject to arbitrary excitation. The fixed and slosh masses, as well as the spring and damping constants, are determined in such a way as to satisfy the principle of equivalence. Numerical simulations illustrate the theoretical results in this paper as well.