Narrow Results

This paper presents an analysis of wave dispersion behavior in electrode–piezoelectric–electrode sandwich structures, considering surface effects (SE). The sandwich structure was situated atop an orthogonally anisotropic viscoelastic substrate. This paper aims to explore the surface effects on the dispersion characteristics of piezoelectric sandwich nanoplates embedded with viscoelastic substrates, integrating frequency-wave number curves and phase velocity-wave number curves. The displacement field of the nanoplate was derived using the sinusoidal shear deformation theory, and governing equations were established through Hamilton’s principle and surface constitutive equations. Subsequently, equations of motion were obtained based on the nonlocal strain gradient theory (NSGT), and characteristic equations were developed using harmonic solutions. The study thoroughly examined the effects of scale, viscoelasticity, and surface properties on wave propagation characteristics. The results reveal that scale effects significantly influence the dispersion curves of nanoplates, depending on the wave number, and emphasize the necessity of considering the surface effects of electrode layers. Notably, a reduction in thickness leads to an upward trend in both frequency and phase velocity curves. Furthermore, the Winkler modulus and shear modulus play a pivotal role in enhancing frequency stiffness, while increases in the damping coefficient and voltage result in a decrease in both frequency and phase velocity.

The paper aims at a numerical study of strength and deformation behaviors of rocks under different loading conditions in uniaxial compression with an elasto-plastic cellular automaton (EPCA^2D) code. Two loading conditions, i.e. with and without considering frictions between loading platens and rock specimen's ends, are used in the failure processes of heterogeneous rocks. Rock specimens are assumed to be the same heterogeneity, i.e. the specimens with different sizes have the same probability of containing flaws. Under this condition, it is concluded that the strength and deformation behaviors of rocks are influenced by the heterogeneity a little. The mismatch of elastic properties of the platen and the rock in influencing the stress distribution at the ends of the specimen is the dominant cause for the so-called strength and deformation size effects, which in turn affects the final failure patterns of rocks.

A new type of cavitation damage has been observed on the turbines installed at the Three Gorges Power Station despite no cavitation detected during model tests. Metallurgical and fluid dynamic analysis suggests that this cavitation is triggered by boundary-layer turbulent production; the damaged (roughened) spot in turn triggers subsequent cavitation (damage) immediately down stream. This forms a sustainable dynamic process, resulting in long and equal-width streamwise damage-strips with spanwise regularity reflecting the spanwise stochastic characteristics of turbulent production. Owing to the heat effect of cavitation, intergranular corrosion takes place through sensitization process, leaving the damaged surface with a corrosion appearance. Also, bluing presents at the damaged tails, owing to the nature of low-intensity damage. Extremely large turbines are much more susceptible to this type of cavitation (damage) owing to the similarity laws currently employed for turbine development not concerning the freestream turbulence and the boundary-layer dynamics.

A non-local elastic shell model is proposed for the first time in this study for considering the small-scale effect in axi-symmetric wave propagation in carbon nanotubes (CNTs). Two coupled radial and longitudinal modes, and one decoupled torsional mode, are derived from the developed non-local shell model. The small-scale effect on wave propagation is numerically studied and discussed. In addition, the cut-off frequency based on the non-local shell model is obtained, which is found to be free of the small-scale effect. It is interesting to note that only one asymptotic phase velocity exists in the CNTs using the non-local shell model, whereas two asymptotic phase velocities can be predicted using the classical or local elastic shell model. It is hoped the research presented herein can be used as a benchmark for future studies on the wave propagation of CNTs with non-local continuum models.

The spatial-varying frequency of a vehicle-bridge interaction (VBI) system subjected to a moving mass is theoretically derived and numerically investigated through a three-dimensional VBI model, in which the effects of moving mass are introduced through the inertial force and centrifugal force in the equation of motion of the bridge. For a large vehicle-to-bridge mass ratio, it has been known that the frequency of a VBI system could change with respect to the location of a moving vehicle. As such, this study derives the analytical solution based on a moving mass-beam system to account for frequency variation and further builds the numerical model with detailed implementation for practical applications. The numerical results show the following findings: (1) The frequency of a VBI system is a function of velocity and location of a moving vehicle. (2) The reduction of spatial-varying frequency ratio for a particular mode decreases with respect to the mode of higher order. (3) The maximum reduction of spatial-varying frequency ratio of the first mode in a moving mass-beam system occurs in the location where the bridge has the maximum deflection as a result of local mode excitation. (4) For the VBI system with high suspension stiffness and large vehicle-to-bridge mass ratio, the absolute variation of spatial-varying frequency ratio of the first mode can be up to 30–40%.

Following the empirical work of Jones (1995a,b) that test the scale effects predicted by the AK models and the R&D based models, this paper tests the scale effects of a major new trade model, the Krugman (1979) version of the Dixit-Stiglitz (1977) model, using the Yang-Heijdra (1993) formula for own price elasticity of demand. Time series data from six economies are used to test the relationships between the average size of firms, population and per capita income. The results show that the scale effects predicted by the revised Krugman model are incompatible with empirical evidence.

A nonlocal Kirchhoff plate model with the van der Waals (vdW) interactions taken into consideration is developed to study the vibration of double-layered graphene sheets (DLGS). The dynamic equations of multi-layered Kirchhoff plate are derived based on strain gradient elasticity. An explicit formula is derived to predict the natural frequency of the DLGS with all edges simply supported. Then a 4-node 24-degree of freedom (DOF) Kirchhoff plate element is developed to discretize the higher order partial differential equations with the small scale effect taken into consideration by the theory of virtual work. It can be directly used to predict the scale effect on the vibrational DLGS with different boundary conditions. A good agreement between finite element method (FEM) results and theoretical natural frequencies of the vibration simply supported double-layered graphene sheet (DLGS) validates the reliability of the FEM. Finally, this new FEM is used to investigate the effect of vdW coefficients, sizes, nonlocal parameters, vibration mode and boundary conditions on the vibration behaviors of DLGS.

The maximum nonbreaking wave height on a horizontal bed is examined through laboratory tests by changing the slope of an approach section from 1/5 to 1/80. As the slope becomes steep, the maximum wave height gradually decreases from the breaker height in water of constant depth: the maximum wave height on the slope 1/80 is about 94% and that on the slope 1/5 is about 80% of the breaker height in water of constant depth. The decrease is induced by the free harmonic waves generated at the junction point of the approach slope and the horizontal bed. Test results also yield a recommendation that the water depth on a horizontal bed be maintained equal to or greater than 10 cm in order to avoid scale effects on wave breaking phenomenon there.

Within the framework of re-modified couple stress theory, the Refined Zigzag Theory is added to the vibration and buckling analysis of sandwich micro-plates embedding functionally graded layers. The disparity between the scale effects along two orthogonal directions is considered through two orthogonal material length scale parameters (MLSPs). Meanwhile, the solutions of natural frequencies and buckling loads show an improved predictive capability through comparing the results with exact and quasi-3D solutions. Two types of functionally graded sandwich micro-plates with simply supported boundary conditions are taken as the illustrative examples, namely, an isotropic functionally grade sandwich micro-plate with a power law and an orthotropic one with an exponential law. The numerical results indicate that the present model can capture the varying scale effects along two orthogonal directions, particularly when the geometric size of the micro-plates is comparable to the MLSPs. When microscopic isotropy is observed, the present model can also make accurate predictions on those kinds of micro-structures by setting the two orthogonal MLSPs equal to each other. In addition, the scale effects are less obvious as the functionally graded sandwich micro-plate is getting thinner and harder; the grading index also has an influence on the scale effects, but this influence is simultaneously depending on the side-to-thickness ratio of the micro-plate.

Accurate estimation of CO₂ emissions is a prerequisite for scientific low-carbon emission policymaking. Based on 20 types of energy consumption data at the prefecture level in China, this paper re-estimates the CO₂ emissions of 198 prefecture-level cities in 2016 by using the method of carbon emission coefficient. The spatial pattern and scale characteristics are analyzed, and the conclusions are as follows: (1) Overall, China’s urban CO₂ emissions show a certain degree of spatial separation in terms of the total amount, per capita emissions, and emission intensity. Cities with the highest CO₂ emissions in China are mainly concentrated in North China, East China and Chongqing, while cities with the highest per capita CO₂ emissions and emission intensity are mainly concentrated in Northwest and North China. (2) Different types of cities have different CO₂ emission characteristics. Resource-based cities have a higher total amount and emission intensity; tourism and underdeveloped cities both have lower values; while super-large-sized cities and many very-large-sized cities have higher CO₂ emissions, but their emission intensities are usually lower; and no obvious rules are found in other cities. (3) Spatial analysis shows that cities with higher CO₂ emissions are clustered. The Beijing–Tianjin–Hebei region, the Yangtze River Delta region, Shandong Province, and Shanxi–Henan–Anhui resource-producing areas are the agglomeration areas of high-emission cities. (4) Scale analysis shows that the characteristics of CO₂ emissions at different scales are different. Provincial-level research can help to identify the environmental impact and total effect of carbon emissions, while urban-scale research is helpful to explore the diversity and phases of cities. Finally, based on the main conclusions of this study, the corresponding urban low-carbon policy implications are drawn.

Because of the non-rivalry of knowledge, the R&D-based endogenous growth model implies the scale effect, which means the larger the population, and the more the number of R&D employees, the faster the economic growth. Although the scale effect is supported by the empirical work of Kremer (1993), Jones (1995a) finds that the experience of OECD countries during the last one hundred years does not show any scale effect. Jones (1995a) and Young (1998), therefore, manage to make some modification to the original R&D-based model to eliminate the scale effect. The modification they make, however, also has some problems. The motivation of this paper is thus to bridge the gap between the R&D-based theoretic model and the empirical facts on scale effect. By introducing the effective time of innovation activity of researchers into the idea production function adopted by the original R&D model, we can get two types of equilibria of economic growth: one with scale effect, the other without it. Thus the model can meet the two ends of contradictive empirical findings of both Kremer (1993) and Jones (1995a, b). To test the model, we simulate the GDP per worker growth rate of 49 countries and check whether the simulated data match the real cross-country data. The results show that our model is better than the Lucas (1988) model and the Romer (1990) model. If the success of the model is judged by the sum of the squared error between the simulated data and the real data, then our model improves the Lucas model and Romer model by at least 20 percent and 59 percent. The policy implication of the model is:in terms of the increase of the economic growth rate, the model suggests that the countries without scale effect should adopt policies to increase the average human capital of the whole population, while the countries with scale effect should increase the number of scientists and engineers as a priority.

The paper aims at a numerical study of strength and deformation behaviors of rocks under different loading conditions in uniaxial compression with an elasto-plastic cellular automaton (EPCA^2D) code. Two loading conditions, i.e. with and without considering frictions between loading platens and rock specimen's ends, are used in the failure processes of heterogeneous rocks. Rock specimens are assumed to be the same heterogeneity, i.e. the specimens with different sizes have the same probability of containing flaws. Under this condition, it is concluded that the strength and deformation behaviors of rocks are influenced by the heterogeneity a little. The mismatch of elastic properties of the platen and the rock in influencing the stress distribution at the ends of the specimen is the dominant cause for the so-called strength and deformation size effects, which in turn affects the final failure patterns of rocks.

The forced mechanism of end milling cutter was further analyzed theoretically when cutting. A force model on micro milling was established. The micro milling experiments were carried out using micro milling cutter. The data of the milling force acting on micro cutter blade was collected and analyzed. The diagram of micro milling force and cutting parameters was intuitively built. The laws on the milling force change were derived from the diagram. The effect of the cutting speed, feed rate and cutting depth on the milling force was got. The results provides the theory basis for t the controlling of machining accuracy in micro-milling.