Nonlinear Dynamic Analysis of Coupled Gear-Rotor-Bearing System with the Effect of Internal and External Excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.

Coupling model for waves propagating over a porous seabed

The wave-seabed interaction issue is of great importance for the design of foundation around marine infrastructures. Most previous investigations for such a problem have been limited to uncoupled or one- way coupled methods connecting two separated wave and seabed sub models with the continuity of pressures at the seabed surface. In this study, a strongly coupled model was proposed to realize both wave and seabed processes in a same program and to calculate the wave fields and seabed response simultaneously. The information between wave fields and seabed fields were strongly shared and thus results in a more profound investigation of the mechanism of the wave-seabed interaction. In this letter, the wave and seabed models were validated with previous experimental tests. Then, a set of application of present model were discussed in prediction of the wave-induced seabed response. Numerical results show the wave-induced liquefaction area of coupled model is smaller than that of uncoupled model.

Sediment mathematical model for sand ridges and sand waves

A new theoretical model is formulated to describe internal movement mechanisms of the sand ridges and sand waves based on the momentum equation of a solid-liquid two-phase flow under a shear flow. Coupling this equation with two-dimensional shallow water equations and wave reflection-diffraction equation of mild slope, a two-dimensional coupling model is established and a validation is carried out by observed hydrogeology, tides,waves and sediment. The numerical results are compared with available observations. Satisfactory agreements are achieved. This coupling model is then applied to the Dongfang 1-1 Gas Field area to quantitatively predict the movement and evolution of submarine sand ridges and sand waves. As a result, it is found that the sand ridges and sand waves movement distance increases year by year, but the development trend is stable.

International progress and evaluation on interactive coupling effects between urbanization and the eco-environment

Global urbanization is exerting severe stress and having far-reaching impacts on the eco-environment, and yet there exists a complex non-linear coupling relationship between the two. Research on the interactive coupling effect between urbanization and the eco-environment will be a popular area of study and frontier in international earth system science and sustainability science in the next 10 years, while also being a high-priority research topic of particular interest to international organizations. This paper systematically collates and summarizes the international progress made in research on interactive coupling theory, coupling relationships, coupling mechanisms, coupling laws, coupling thresholds, coupling models and coupling optimization decision support systems. The research shows that urbanization and eco-environment interactive coupling theories include the Kuznets curve theory, telecoupling theory, planetary boundaries theory, footprint family theory and urban metabolism theory; most research on interactive coupling relationships is concerned with single- element coupling relationships, such as those between urbanization and water, land, atmosphere, climate change, ecosystems and biodiversity; the majority of research on interactive coupling mechanisms and laws focuses on five research paradigms, including coupled human and nature systems, complex social-ecological systems, urban ecosystems, social-economic-natural complex ecosystems, and urbanization development and eco-environment constraint ring; the majority of interactive coupling simulations use STIRPAT models, coupling degree models, multi-agent system models and big data urban computer models; and research has been carried out on urbanization and eco-environment coupling thresholds, coercing risk and optimal decision support systems. An objective evaluation of progress in international research on interactive coupling between urbanization and the eco-environment suggests that there are six main research focal points and six areas lacking research： a lot of research exists on macroscopic coupling effects, with little research on urban agglomeration and scale coupling effects; considerable research exists on sin-gle-dimension coupling effects, with little on multiple-dimension coupling effects; a great deal exists on ＂one-to-one＂ dual- element coupling effects, with little on ＂many-to-many＂ multiple-element coupling effects; a lot exists on positive feedback coupling effects, and little on negative feedback coupling effects; a great deal exists on empirical coupling effects, and little on theoretical coupling effects; a great deal exists on the use of simple quantitative methods, and little on using integrated simulation methods. Future studies should focus on coupling effects between urbanization in urban agglomerations and the eco-environment, spatial scale coupling effects, multi-dimensional coupling effects, telecoupling effects, ＂one-to-many＂ and ＂many-to-many＂ element coupling effects, and positive and negative feedback coupling effects. There is also a need to strengthen the development and application of dynamic models for multi-element,-scale,-scenario,-module and-agent integrated spatiotemporal coupling systems and further improve theoretical innovations in coupling effect research and integrate and form complete and diverse coupling theoretical systems.