Research on the FE and semi-analytical solution with the blade-casing rub-impact dynamical system

Based on the elasticity theory, a differential equation of forced oscillation of the blade-casing system with rub-impact excitation was deduced, and the steady analytic solution was derived. The analytic solution was verified with the FE (finite element) method, the results indicated that the eigenvalues of dynamical equation by FE method are larger than the semi-analytical method’s, while the vibration modes are identical. Due to the characteristics of rub-impact excitation between the blade and casing, it is not suitable to solve impacting vibrational response for rotating blade with the steady analytic solution. Therefore, the semi-analytical solution was adopted to solve these dynamic problems, which can get the vibration response of any position for its continuity characteristic. Then, the FE and semi-analytical method is used. The comparison of dynamical response with changing speed, rub-impact depth and the friction coefficient was investigated in details. It is found that the speed has the greater effect on the dynamical vibration response, but other parameters affect the response slightly at the same rotational speed. When the friction coefficient and rub-impact depth unchanging, with the increasing speed, the contribution of each multi-frequency component to the resonant response grows obviously, especially the high-harmonic components should be pay more attention. Blade-casing model is easy to form a new resonance system, which will appear different resonant response with the increasing friction coefficient. When the friction coefficient reaches to a certain value, the response amplitude tends to be stable

Nonlinear Dynamic Behavior Analysis of Pressure Thin-Wall Pipe Segment with Supported Clearance at Both Ends

An analysis of nonlinear behaviors of pressure thin-wall pipe segment with supported clearance at both ends was presented in this paper. The model of pressure thin-wall pipe segment with supported clearance was established by assuming the restraint condition as the work of springs in the deformation directions. Based on Sanders shell theory, Galerkin method was utilized to discretize the energy equations, external excitation, and nonlinear restraint forces. And the nonlinear governing equations of motion were derived by using Lagrange equation. The displacements in three directions were represented by the characteristic orthogonal polynomial series and trigonometric functions. The effects of supporting stiffness and supported clearance on dynamic behavior of pipe wall were discussed. The results show that the existence of supported clearance may lead to the changing of stiffness of the pipe vibration system and the dynamic behaviors of the pipe system show nonlinearity and become more complex; for example, the amplitude-frequency curve of the foundation frequency showed hard nonlinear phenomenon. The chaos and bifurcation may emerge at some region of the values of stiffness and clearance, which means that the responses of the pressure thin-wall pipe segment would be more complex, including periodic motion, times periodic motion, and quasiperiodic or chaotic motions

Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition

Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed

Can Low-Carbon Pilot City Policies Effectively Promote High-Quality Urban Economic Development?—Quasi-Natural Experiments Based on 227 Cities

To explore the relationship between low-carbon pilot city policies (LCC) and the high-quality development of urban economy, this paper calculates the high-quality development index based on five dimensions to construct a double-difference model for empirical research, taking the data of 227 cities in China from 2004 to 2019 and the second batch of low-carbon pilot cities as the main research object. The research conclusions are as follows: (1) The LCC has promoted the high-quality economic development of the pilot cities, and has long-term effects, which are mainly reflected in three dimensions: Innovative development, residents’ life, and urban public services. (2) The promotion effect is mainly reflected in the big cities, as well as the eastern and central regions. (3) The intermediary function is embodied in three aspects: Industrial upgrading, urban technological innovation, and urban investment

Can Low-Carbon Pilot City Policies Effectively Promote High-Quality Urban Economic Development?—Quasi-Natural Experiments Based on 227 Cities

To explore the relationship between low-carbon pilot city policies (LCC) and the high-quality development of urban economy, this paper calculates the high-quality development index based on five dimensions to construct a double-difference model for empirical research, taking the data of 227 cities in China from 2004 to 2019 and the second batch of low-carbon pilot cities as the main research object. The research conclusions are as follows: (1) The LCC has promoted the high-quality economic development of the pilot cities, and has long-term effects, which are mainly reflected in three dimensions: Innovative development, residents’ life, and urban public services. (2) The promotion effect is mainly reflected in the big cities, as well as the eastern and central regions. (3) The intermediary function is embodied in three aspects: Industrial upgrading, urban technological innovation, and urban investment

Nonlinear Vibration Analysis of a Rotating Disk-Beam System Subjected to Dry Friction

In this work, a continuum model is proposed to simulate and interpret the coupling vibration characteristics of a rotating disk-beam system with the dovetail interfaces. The dovetail interface feature is represented by a macroslip dry friction model. The present study also derives a new mode function to simulate the vibration of a rotating beam with loosely assembled dovetail attachment. The new proposed mode function is validated by comparing the natural characteristics and vibration response with those obtained from a finite element (FE) model. At last, based on the nonlinear response results obtained by the Newmark-β method, the effects of different parameters on the nonlinear dynamics of the coupling system are discussed. The following interesting phenomena have been revealed: the flexible disk can impose different influences on the response characteristics of the rotating beam. The effects of dry friction on the beam’s energy dissipation are significant, especially at a low rotational speed. Further analysis yields that the excitation level and friction coefficient also exhibit a significant impact on the damping effect of dry friction. Consequently, it should be noted that the optimal values of the contact surface’s parameters allow achieving a better damping effect in the engineering practice

Growth Responses and Root Characteristics of Lettuce Grown in Aeroponics, Hydroponics, and Substrate Culture

Aeroponics is a relatively new soilless culture technology which may produce food in space-limited cities or on non-arable land with high water-use efficiency. The shoot and root growth, root characteristics, and mineral content of two lettuce cultivars were measured in aeroponics, and compared with hydroponics and substrate culture. The results showed that aeroponics remarkably improved root growth with a significantly greater root biomass, root/shoot ratio, and greater total root length, root area, and root volume. However, the greater root growth did not lead to greater shoot growth compared with hydroponics, due to the limited availability of nutrients and water. It was concluded that aeroponics systems may be better for high value true root crop production. Further research is necessary to determine the suitable pressure, droplet size, and misting interval in order to improve the continuous availability of nutrients and water in aeroponics, if it is to be used to grow crops such as lettuce for harvesting above-ground parts

A Comparison Study of the Nutrient Fluxes in a Newly Impounded Riverine Lake (Longjing Lake): Model Calculation and Sediment Incubation

Diffusion flux is an essential tool to estimate the contribution of internal nitrogen and phosphorus in eutrophic lakes. There are mainly two methods, i.e., model calculation based on in-situ porewater sampling and water quality monitoring in laboratory incubation. The results obtained by the two methods are rarely compared, decreasing the validity of internal contribution and following management strategies. In this study, sediment samples were collected from a lake in China, then the fluxes were estimated by model calculation and laboratory incubation. The results show that there is an order of magnitude difference in the fluxes measured by these two methods. The mean values of ammonia (NH4+-N) and soluble reactive phosphate (SRP) obtained from the model calculations were 24.4 and 1.30, respectively. The mean values of NH4+-N and SRP obtained in the undisturbed group of sediment incubation were 7.84 and 5.47, respectively, and in the disturbed group of sediment incubation were 16.2 and 4.06, respectively. Sediment incubation is a combination of multiple influencing factors to obtain fluxes, while porewater model is based on molecular diffusion as the theoretical basis for obtaining fluxes. According to the different approaches of the two methods, sediment incubation is recommended as a research tool in lake autochthonous release management when the main objective is to remove pollution, while the porewater model is recommended as a research tool when the main objective is to control pollution. When assessing the diffusive flux of nitrogen, it is recommended to choose the stable form of total dissolved nitrogen to discuss the flux results