Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given. (C) 2002 Published by Elsevier Science Ltd.

Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

The mechanism of energy loss and transition in a flow with submerged vegetation

The mechanism of energy balance in an open-channel flow with submerged vegetation was investigated. The energy borrowed from the local flow, energy spending caused by vegetation drag and flow resistance, and energy transition along the water depth were calculated on the basis of the computational results of velocity and Reynolds stress. Further analysis showed that the energy spending in a cross-section was a maximum around the top of the vegetation, and its value decreased progressively until reaching zero at the flume bed or water surface. The energy borrowed from the local flow in the vegetated region could not provide for spending; therefore, surplus borrowed energy in the non-vegetated region was transmitted to the vegetated region. In addition, the total energy transition in the cross-section was zero; therefore, the total energy borrowed from the flow balanced the energy loss in the whole cross-section. At the same time, we found that there were three effects of vegetation on the flow: turbulence restriction due to vegetation, turbulence source due to vegetation and energy transference due to vegetation, where the second effect was the strongest one. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

Surface energy partitioning in alpine swamp meadow in the Qinghai Tibetan Plateau

Based on surface energy flux data measured by eddy covariance methods from China Flux in alpine swamp meadow of the Qinghai Tibetan Plateau in 2005, the daily and seasonal dynamic of surface energy fluxes and their partitioning, as well as abiotic factors effects were analyzed. The results suggested that LE （Latent heat flux） was the largest consumer of the incoming energy. Rn （Net radiation flux） and LE showed clear seasonal variations in sharp hump and up to their maximums in August and July, respectively. H （Sensible heat flux） increased to its peak in August whereafter declined slowly. Precipitation could reduce the components of surface energy. As to Rn and LE, their correlations with abiotic factors were evident while it was not significant in H. Average EBR （Energy balance ratio） was 50.7 %, which was much larger in growing season than non-growing season.

Seasonal and interannual variation in water vapor and energy exchange over a typical steppe in Inner Mongolia, China

In this study, we conducted eddy covariance (EC) measurements of water vapor exchange over a typical steppe in a semi-arid area of the Inner Mongolia Plateau, China. Measurement sites were located within a 25-year-old enclosure with a relatively low leaf area index (similar to 1. 5 m(2) m(-2)) and dominated by Leymus chinensis. Energy balance closure was (H + LE) = 17.09 + 0.69 x (Rn - G) (W/m(2); r(2) = 0.95, n = 6596). Precipitation during the two growing seasons of the study period was similar to the long-term average. The peak evapotranspiration in 2004 was 4 mm d(-1), and 3.5 mm d(-1) in 2003. The maximum latent heat flux was higher than the sensible heat flux, and the sensible heat flux dominated the energy budget at midday during the entire growing season in 2003; latent heat flux was the main consumption component for net radiation during the 2004 growing season. During periods of frozen soil in 2003 and 2004, the sensible heat flux was the primary consumption component for net radiation. The soil heat flux component was similar in 2003 and 2004. The decoupling coefficient (between 0.5 and 0.1) indicates that evapotranspiration was strongly controlled by saturation water vapor pressure deficit (VPD) in this grassland. The results of this research suggest that energy exchange and evapotranspiration were controlled by the phenology of the vegetation and soil water content. In addition, the amount and frequency of rainfall significantly affect energy exchange and evapotranspiration upon the Inner Mongolia plateau. (c) 2007 Published by Elsevier B.V.

Energy exchange between the atmosphere and a meadow ecosystem on the Qinghai-Tibetan Plateau

To reveal the potential contribution of grassland ecosystems to climate change, we examined the energy exchange over an alpine Kobresia meadow on the northeastern Qinghai-Tibetan Plateau. The annual pattern of energy exchange showed a clear distinction between periods of frozen soil with the daily mean soil temperature at 5 cm (T-s5 ≤ 0 ° C) and non-frozen soil (T-s5 > 0 ° C). More than 80% of net radiation was converted to sensible heat (H) during the frozen soil period, but H varied considerably with the change in vegetation during the non-frozen soil period. Three different sub-periods were further distinguished for the later period: (1) the pre-growth period with Bowen ratio (β) > 1 was characterized by a high β of 3.0 in average and the rapid increase of net radiation associated with the increases of H, latent heat (LE) and soil heat; (2) during the Growth period when β ≤ 1, the LE was high but H fluxes was low with β changing between 0.3 and 0.4; (3) the post-growth period with average β of 3.6 when H increased again and reached a second maximum around early October. The seasonal pattern suggests that the phenology of the vegetation and the soil water content were the major factors affecting the energy partitioning in the alpine meadow ecosystem. © 2005 Elsevier B.V. All rights reserved.

Effects of Subgrid-Scale Modeling on Time Correlations in Large Eddy Simulation

The effects of the unresolved subgrid-scale (SGS) motions on the energy balance of the resolved scales in large eddy simulation (LES) have been investigated actively because modeling the energy transfer between the resolved and unresolved scales is crucial to constructing accurate SGS models. But the subgrid scales not only modify the energy balance, they also contribute to temporal decorrelation of the resolved scales. The importance of this effect in applications including the predictability problem and the evaluation of sound radiation by turbulent flows motivates the present study of the effect of SGS modeling on turbulent time correlations. This paper compares the two-point, two-time Eulerian velocity correlation in isotropic homogeneous turbulence evaluated by direct numerical simulation (DNS) with the correlations evaluated by LES using a standard spectral eddy viscosity. It proves convenient to express the two-point correlations in terms of spatial Fourier decomposition of the velocity field. The LES fields are more coherent than the DNS fields: their time correlations decay more slowly at all resolved scales of motion and both their integral scales and microscales are larger than those of the DNS field. Filtering alone is not responsible for this effect: in the Fourier representation, the time correlations of the filtered DNS field are identical to those of the DNS field itself. The possibility of modeling the decorrelating effects of the unresolved scales of motion by including a random force in the model is briefly discussed. The results could have applications to the problem of computing sound sources in isotropic homogeneous turbulence by LES

General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.

Non-Slipping Jkr Model For Transversely Isotropic Materials

A generalized plane strain JKR model is established for non-slipping adhesive contact between an elastic transversely isotropic cylinder and a dissimilar elastic transversely isotropic half plane, in which a pulling force acts on the cylinder with the pulling direction at an angle inclined to the contact interface. Full-coupled solutions are obtained through the Griffith energy balance between elastic and surface energies. The analysis shows that, for a special case, i.e., the direction of pulling normal to the contact interface, the full-coupled solution can be approximated by a non-oscillatory one, in which the critical pull-off force, pull-off contact half-width and adhesion strength can be expressed explicitly. For the other cases, i.e., the direction of pulling inclined to the contact interface, tangential tractions have significant effects on the pull-off process, it should be described by an exact full-coupled solution. The elastic anisotropy leads to an orientation-dependent pull-off force and adhesion strength. This study could not only supply an exact solution to the generalized JKR model of transversely isotropic materials, but also suggest a reversible adhesion sensor designed by transversely isotropic materials, such as PZT or fiber-reinforced materials with parallel fibers. (c) 2007 Elsevier Ltd. All rights reserved.

Formation Mechanism Of Lamellar Chips During Machining Of Bulk Metallic Glass

The uniqThe unique lamellar chips formed in turning–machining of a Vit 1 bulk metallic glass (BMG) are found to be due to repeated shearband formation in the primary shear zone (PSZ). A coupled thermomechanical orthogonal cutting model, taking into account force, free volume and energy balance in the PSZ, is developed to quantitatively characterize lamellar chip formation. Its onset criterion is revealed through a linear perturbation analysis. Lamellar chip formation is understood as a self-sustained limit-cycle phenomenon: there is autonomous feedback in stress, free volume and temperature in the PSZ. The underlying mechanism is the symmetry breaking of free volume flow and source, rather than thermal instability. These results are fundamentally useful for machining BMGs and even for understanding the physical nature of inhomogeneous flow in BMGs.ue lamellar chips formed in turning–machining of a Vit 1 bulk metallic glass (BMG) are found to be due to repeated shearband.

On the origin of shear banding instability in metallic glasses

To uncover the physical origin of shear-banding instability in metallic glass (MG), a theoretical description of thermo-mechanical deformation of MG undergoing one-dimensional simple shearing is presented. The coupled thermo-mechanical model takes into account the momentum balance, the energy balance and the dynamics of free volume. The interplay between free-volume production and temperature increase being two potential causes for shear-banding instability is examined on the basis of the homogeneous solution. It is found that the free-volume production facilitates the sudden increase in the temperature before instability and vice versa. A rigorous linear perturbation analysis is used to examine the inhomogeneous deformation, during which the onset criteria and the internal length and time scales for three types of instabilities, namely free-volume softening, thermal softening and coupling softening, are clearly revealed. The shear-banding instability originating from sole free-volume softening takes place easier and faster than that due to sole thermal softening, and dominates in the coupling softening. Furthermore, the coupled thermo-mechanical shear-band analysis does show that an initial slight distribution of local free volume can incur significant strain localization, producing a shear band. During such a localization process, the local free-volume creation occurs indeed prior to the increase in local temperature, indicating that the former is the cause of shear localization, whereas the latter is its consequence. Finally, extension of the above model to include the shear-induced dilatation shows that such dilatation facilitates the shear instability in metallic glasses.

暖温带落叶阔叶混交林能量生态学研究

本文是首篇研究中国暖温带落叶阔叶混交林能量生态学的论文。在文中，笔者以详实的第一手资料从能量环境、能量流动、能量组合以及能量平衡几个方面，全面、系统地阐述、分析了辽东栎林——这一暖温带落叶阔叶混交林典型自然群落代表的能量生态学特征。 在能量环境一章中，笔者从能量流动，能量平衡的角度出发重点研究了辽东栎群落的辐射能量环境特征。笔者以1991-1993年的观测资料为基础，从乔木、灌木和草本三个层次分析了生长季总辐射、散射辐射、直射辐射、反射辐射、净辐射、先合有效辐射、透射辐射、吸收辐射以及乔木层和灌木层反射率的季节动态和日进程特征，并从天文因子、气象因子和群落自身发育特征几方面解释分析了辐射能量环境的这种时空动态特征，同时，分析了这种变化特征对群落能量流动、分配和平衡过程可能产生的影响。 另外，笔者也对群落湿度和风速环境的时空动态特征进行了分析。 在能量流动一章，笔者以1992-1993年的野外实验资料为依据，沿季节动态、月际变化和日进程的时间轴，从群落、乔木层、灌木层、草本层以及各乔、灌木种群的空间尺度详细分析、阐述了太阳辐射能在森林群落内的流动和转化特征，并从能量环境和群落发育的角度解释分析了能量在群落内的这种时空分布和转化特征。所讨论的能流对象包括群落、乔、灌、草各层及各乔、灌木种群的总能流固定量、叶片呼吸耗能量、剩余能流固定量以及沿枯枝落叶流出的能流量。 与分析能流过程同步，笔者从上述的时、空尺度分别以生长季内太阳总辐射和光合有效辐射为基础计算、分析了森林群落的光能转化率特征。 在这一章的最后，笔者概述性地介绍了辽东栎群落的能量平衡特征 在第四章，笔者从能值的角度出发，以能量密度为标准讨论了能量沿群落各层及各乔、灌木种群的积累、分配和组合特征，并讨论了能量流动和光能转化率与热值和能量密度的关系。 辽东栎群落能量生态学的研究不但为了解暖温带落叶阔叶林生态系统的结构和功能，为恢复和重建退化的森林生态系统提供了丰富详实的理论信息，而且，也为山区人工林优化模式的组建提供了理论依据和实践指南。

暖温带山地森林生态系统水分问题研究

本文的研究是中国科学院院重大项目“暖温带森林生态系统结构、功能及生产力持续发展”的主要内容之一。作者以详实的第一手资料，从森林小气候及环境特征、森林降水的水文学效应及降水化学、森林的热量平衡及蒸发散、树木个体的水分生理生态学几个方面阐述、分析了暖温带山地森林生态系统主要林分的水分及其相关生态学问题。 在森林小气候及环境特征一章，作者从不同季节的日变化和生长季的月际变化两个视角，以落叶阔叶混交林和油松林为研究对象，考察了林冠上和林下四个不同梯度的风速、气温、湿度、地温的时空动态。 在森林降水的水文学效应和降水化学一章，笔者以1993、1994年试验年度的83次降雨观测资料为基础，分析了暖温带落叶阔叶混交林、辽东栎林、油松林、落叶松林、次生灌丛降水总量与各降水分量的关系，建立了单次降雨与各降雨分量的经验模型，并给出了生长季林冠作用层和林地作用层的水量分配的月际动态。在探讨上述水量关系的同时，作者还分析了前四类林分大气降水及各降水分量中N、K、Ca、S、Mg、P、Al七种元素的浓度及含量变化，就不同树种对上述元素的选择性交换作了探讨，比较了不同林分的降水化学效应差异。 在第四章，作者以落叶阔叶混交林和油松林为研究对象，分析了两类林分在94试验年度生长季辐射平衡、显热通量、潜热通量、蒸发散以及土壤热通量的季节变化和日变化特征。 在树木个体的水分生理生态部分，作者应用压力室一容积技术测定了暖温带落叶阔叶林、油松林和次生灌丛10种主要树种的水分生理指标：日最低水势值、最大膨压时的渗透势、膨压为零时的渗透势、初始质壁分离时渗透水的相对含量、初始质壁分离时的相对含水量、质外体水的相对含量、细胞最大弹性模量，并比较了不同树种间上述指标与抗旱性的关系。此外，作者还应用Li-1600稳态气孔计测定了上述林分中主要树种的日均蒸腾强度的季节动态，并比较了上下两面叶片蒸腾特性的差异。最后，作者采用九种水分生理指标对10种主要树种的抗旱性作了主分量分析，给出了综合性抗旱指标。 在第六章，作者应用热脉冲技术系统地研究了暖温带山地森林主要乔木树种的树干液流的时空变化特征，并应用时序分析方法对上述树种的树液流量变化建立了自回归模型，在此基础上提出了生理惯性指标，给予了生理学解释。