The geometric structure and dynamic properties of lauwerier attractor

 Introduction The strange chaotic attractor (ACS) is an important subject in the nonlinear field. On the basis of the theory of transversal heteroclinic cycles, it is suggested that the strange attractor is the closure of the unstable manifolds of countable infinite hyperbolic periodic points. From this point of view some nonlinear phenomena are explained reasonably. 更多还原

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

The dynamic evolution of the kepler supernova remnant

been analyzed in detail. The effects ofm icroscopic energy transfer from

Dynamic-response of a laminated plate with friction damping

Nonlinear Dynamic Response of Tension Leg Platform

Tension Leg Platform (TLP) is a typical compliant offshore structure for oil exploitation in deep water. Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that displacements (translations and rotations) are small magnitude. Herein a theoretical method for analyzing the nonlinear dynamic behavior of TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e. finite displacement, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. Using this theoretical model, we perform the numerical analysis of dynamic response of a representative TLP. The comparison between the degenerative linear solution of the proposed nonlinear model and the published one shows good agreements. Furthermore, numerical results are presented which illustrate that nonlinearities exert a distinct influence on the dynamic responses of the TLP.

Nonlinear Dynamic Responses of the Tensioned Tether under Parametric Excitations

The nonlinear dynamic responses of the tensioned tether subjected to combined surge and heave motions of floating platform are investigated using 2-D nonlinear beam model. It is shown that if the transverse-axial coupling of nonlinear beam model and the combined surge-heave motions of platform are considered, the governing equation is not Mathieu equation any more, it becomes nonlinear Hill equation. The Hill stability chart is obtained by using the Hill's infinite determinant and harmonic balance method. A parameter M, which is the function of tether length, the surge and heave amplitude of platform, is defined. The Hill stability chart is obviously different from Mathieu stability chart which is the specific case as M=0. Some case studies are performed by employing linear and nonlinear beam model respectively. It can be found that the results differences between nonlinear and linear model are apparent.

Comparisons of static, quasi-static and dynamic 3D porous media scale network models for two-phase immiscible flow in porous media

A dynamic 3D pore-scale network model is formulated for investigating the effect of interfacial tension and oil-water viscosity during chemical flooding. The model takes into account both viscous and capillary forces in analyzing the impact of chemical properties on flow behavior or displacement configuration, while the static model with conventional invasion percolation algorithm incorporates the capillary pressure only. From comparisons of simulation results from these models. it indicates that the static pore scale network model can be used successfully when the capillary number is low. With the capillary increases due to the enhancement of water viscosity or decrease of interfacial tension, only the quasi-static and dynamic model can give insight into the displacement mechanisms.

Effects of fundamental structure parameters on dynamic responses of submerged floating tunnel under hydrodynamic loads

This paper investigates the effects of structure parameters on dynamic responses of submerged floating tunnel (SFT) under hydrodynamic loads. The structure parameters includes buoyancy-weight ratio (BWR), stiffness coefficients of the cable systems, tunnel net buoyancy and tunnel length. First, the importance of structural damp in relation to the dynamic responses of SFT is demonstrated and the mechanism of structural damp effect is discussed. Thereafter, the fundamental structure parameters are investigated through the analysis of SFT dynamic responses under hydrodynamic loads. The results indicate that the BWR of SFT is a key structure parameter. When BWR is 1.2, there is a remarkable trend change in the vertical dynamic response of SFT under hydrodynamic loads. The results also indicate that the ratio of the tunnel net buoyancy to the cable stiffness coefficient is not a characteristic factor affecting the dynamic responses of SFT under hydrodynamic loads.

Influences of Structural Damping and Buoyancy-Weight Ratio on Dynamic Responses of Submerged Floating Tunnel

The recent progress of submerged floating tunnel (SFT) investigation and SFT prototype (SFTP) project in Qiandao Lake (Zhejiang Province, P.R. China) is the background of this research. Structural damping effect is brought into present computation model in terms of Rayleigh damping. Based on the FEM computational results of SFTPs as a function of buoyancy-weight ratio (BWR) under hydrodynamic loads, the effect of BWR on the dynamic response of SFT is illustrated. In addition, human comfort index is adopted to discuss the comfort status of the SFTP.

Nonlinear Dynamic Responses of Tension Leg Platform with Slack-Taut Tether

The slack-taut state of tether is a particular Averse circumstance, which may influence the normal operation stale of tension leg platform (TLP). The dynamic responses of TLP with slack-taut tether are studied with consideration of several nonlinear factors introduced by large amplitude motions. The time histories of stresses of tethers of a typical TLP in slack-taut state are given. In addition, the sensitivities of slack to stiffness and mass are investigated by varying file stiffness of tether and mass of TLP. It is found that slack is sensitive to the mass of TLP. The critical culled surfaces (over which indicates the slack) for the increase of mass are obtained.

Numerical Simulation of Liquefaction Deformation of Sand Layer around Bucket Foundations under Dynamic Loadings

Bucket Foundations under Dynamic Loadings The liquefaction deformation of sand layer around a bucket foundation is simulated under equivalent dynamic ice-induced loadings. A simplified numerical model is presented by taking the bucket-soil interaction into consideration. The development of vertical and horizontal liquefaction deformations are computed under equivalent dynamic ice-induced loadings. Firstly, the numerical model and results are proved to be reliable by comparing them with the centrifuge testing results. Secondly, the factors and the development characteristics of liquefaction deformation are analyzed. Finally, the following numerical simulation results are obtained: the liquefaction deformation of sand layer increases with the increase of loading amplitude and with the decrease of loading frequency and sand skeleton’s strength. The maximum vertical deformation is located on the sand layer surface and 1/4 times of the bucket’s height apart from the bucket’s side wall (loading boundary). The maximum horizontal deformation occurs at the loading boundary. When the dynamic loadings is applied for more than 5 hours, the vertical deformation on the sand layer surface reaches 3 times that at the bottom, and the horizontal deformation at 2.0 times of the bucket height apart from the loading boundary is 3.3% of which on the loading boundary.

Experimental Study on the Responses of Bucket Foundations in Calcareous Sand under Vertical Dynamic Loading

Abstract: Experiments to determine the vertical static bearing capacity are carried out first in laboratory which is taken as a reference for choosing the amplitudes of vertical dynamic loading. Then a series of experiments are carried out to study the influences of factors, such as the scales of bucket, the amplitude and frequency of loading, the density of soils etc.. According to the experimental results, the responses of bucket foundations in calcareous sand under vertical dynamic loadings are analyzed. It is shown that there exists a limited effected zone under vertical dynamic loading. The scale of this zone is about one times of the bucket’s height. In this zone, the density of soil layer, the deformation and the pore pressure change obviously.

Response of the Bucket Foundation in Calcareous Sand under Horizontal Dynamic Load

Abstract: Experiments to determine the horizontal static bearing capacity are carried out first. The static bearing capacity is a reference for choosing the amplitudes of dynamic load. Then a series of experiments under dynamic horizontal load are carried out in laboratory to study the influences of factors, such as the scales of bucket, the amplitude and frequency of load, the density of soils etc.. The responses of bucket foundations in calcareous sand under horizontal dynamic load are analyzed according to the experimental results. The displacements of bucket and sand layer are analyzed.

Dimensionless Analysis of the Simulation of Bucket Foundations under Dynamic Load

Firstly, the main factors are obtained by use of dimensionless analysis. Secondly, the time scaling factors in centrifuge modeling of bucket foundations under dynamic load are analyzed based on dimensionless analysis and control- ling equation. A simplified method for dealing with the conflict of scaling factors of the inertial and the percolation in sand foundation is presented. The presented method is that the material for experiments is not changed while the effects are modified by perturbation method. Thirdly, the characteristic time of liquefaction state and the characteristic scale of affected zone are analyzed.