superposition principle
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Author(s):  
S. Şule Şener Kiliç

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.


Micromachines ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 66
Author(s):  
Xinyue Bian ◽  
Fengqin Li ◽  
Yongjun Jian

In this paper, the effects of asymmetrically modulated charged surfaces on streaming potential, velocity field and flow rate are investigated under the axial pressure gradient and vertical magnetic field. In a parallel-plate microchannel, modulated charged potentials on the walls are depicted by the cosine function. The flow of incompressible Newtonian fluid is two-dimensional due to the modulated charged surfaces. Considering the Debye–Hückel approximation, the Poisson–Boltzmann (PB) equation and the modified Navier–Stokes (N-S) equation are established. The analytical solutions of the potential and velocities (u and v) are obtained by means of the superposition principle and stream function. The unknown streaming potential is determined by the condition that the net ionic current is zero. Finally, the influences of pertinent dimensionless parameters (modulated potential parameters, Hartmann number and slip length) on the flow field, streaming potential, velocity field and flow rate are discussed graphically. During the flow process and under the impact of the charge-modulated potentials, the velocity profiles present an oscillating characteristic, and vortexes are generated. The results show that the charge-modulated potentials are beneficial for the enhancement of the streaming potential, velocity and flow rate, which also facilitate the mixing of fluids. Meanwhile, the flow rate can be controlled through the use of a low-amplitude magnetic field.


2021 ◽  
Author(s):  
Bikash Chandra Chakraborty

Fiber Reinforced Plastics (FRPs) are widely used in marine sector owing to their high specific strength and resistance to marine corrosion. For naval application, additional advantages are transparency to radar wave and better vibration damping than metals. The use of various FRPs in off-shore structures and marine vessels needs analysis of desired properties considering the types of matrices and fiber. The common consideration is effect of sea water on the properties of the FRP. This chapter gives a brief on use of different FRPs in various areas such as off-shore pillars, Reinforced Cement Concrete (RCC) enclosers, primary and secondary marine components. A brief discussion is included here on diffusion models and estimation of durability by a time-temperature superposition principle applied to water ingress and corresponding change in mechanical strength of FRPs with examples. The effect of microbial activity on the damage of FRP is not very much reported in literature. It is known that sulfate-reducing bacteria (SRB) are the most damaging microbes for FRP. In conclusion, it is highlighted that vinyl-ester-based FRPs using glass and carbon fibers are best for marine application. To determine the realistic service life in marine environment, Vinyl Ester- FRP (VE-FRP) are to be simultaneously studied for damage due to sea water and the microbes such SRB.


Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 119
Author(s):  
Hong-Jun Noh ◽  
Hun-Bong Lim ◽  
Hee-Chan Yoon ◽  
Young-Hwan Han ◽  
Hyun-Ik Yang

In the shipbuilding industry, welding is the main technique used to join steel structures. There is a lifting process, post-welding, that can eliminate the correction effect of line heating. Line heating is reperformed after the lifting process. This can significantly delay the ship assembly process. Herein, we present a design method for installing a permanent stiffener to avoid the disappearance of the line heating effect during the lifting process. The change in physical properties due to heating and cooling of the line heating is calculated. The limiting stress, at which the effect of the line heating completely disappears, based on the inherent strain theory, is obtained. The phase fraction by the cooling rate is calculated using the continuous cooling transformation diagram and the Kiustinen–Marburgerm equation. Physical properties affected by the phase transformation are calculated, considering the physical properties and fraction of each phase. The square plate theory and superposition principle are used to construct a local model, with a stiffener, of the ship block. The stress caused by the shape of the stiffener and the distance between the stiffeners were calculated for the local model. The calculated stress and the limiting stress were compared to determine, for the expected line heating efficiency, the most acceptable stiffener design. Finally, to confirm the elimination of the problem, the designed stiffener is analyzed using the finite element method.


Author(s):  
Kunheng Li ◽  
Zhiyong Chen ◽  
Wenku Shi

Abstract With focus on quickly and accurately predicting and evaluating the aging performance degradation of rubber at room temperature, the pseudo-failure life at each different acceleration temperature is proposed to be calculated by interpolation method based on indoor high temperature accelerated aging data, and on the basis of the obtained pseudo-failure life.By introducing the time–temperature equivalence principle, a shift factor obeying to an Arrhenius law is derived, and master curves are built as well for the compression set as for the ultimate mechanical properties.The concept of the sum of squares of dispersion coefficient errors is proposed to evaluate the prediction accuracy.Meanwhile a quantitative calculation method that considers the effect of temperature on the performance degradation curve and the shift factor is innovatively proposes.The results show that the proposed optimization method based on the traditional time-temperature superposition principle can quickly process the aging life at room temperature, and the prediction results are distributed within the 3-fold dispersion line, which can well meet the engineering requirements. The reduction of the DSC value from 1.4164 to 1.0828 further demonstrates the effectiveness of the proposed method above. This method can provide some reference for other related polymer materials accelerated aging data processing and life prediction.


Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 19
Author(s):  
Chiara Tozzi ◽  
Davide Dalmazzo ◽  
Orazio Baglieri ◽  
Ezio Santagata

The research described in this paper deals with the experimental evaluation and modeling of physical hardening in asphalt binders. The term physical hardening refers to a reversible phenomenon occurring at low temperatures that causes time-dependent changes in viscoelastic properties. The experimental approach, followed to quantitatively assess physical hardening, was based on flexural creep tests carried out by means of the Bending Beam Rheometer at various temperatures and conditioning times. The results obtained confirmed that hardening phenomena have a significant influence on the creep response of asphalt binders, to an extent that can be quantitatively assessed by referring to the appropriate rheological parameters and by applying the loading time–conditioning time superposition principle. The experimental data were fitted to a mechanical model proposed in the literature (composed of a single Kelvin–Voigt element) and thereafter to an improved model (with two Kelvin–Voigt elements in series). Both models were assessed in terms of their prediction accuracy. The improved model was found to better describe physical hardening effects in the case of both short- and long-term conditioning. Practical implications of the study were finally highlighted by referring to possible ranking criteria to be introduced in acceptance procedures for the comparative evaluation of asphalt binders.


2021 ◽  
Author(s):  
Shijun Huang ◽  
Yuanrui Zhu ◽  
Shichao Chai ◽  
Guanyang Ding ◽  
Yicheng Xin ◽  
...  

Abstract A major concern with water injection in offshore oil reservoir is the water breakthrough. The formation heterogeneity is the main reason for it. In order to evaluate the water injection efficiency, a visualized 2-D experiment was carried out to obtain the distribution law of injected water and the variation of injection parameters in homogeneous and heterogeneous formation. In addition, a coupled wellbore/reservoir model was established by applying microelement method, superposition principle and imaging. This model considers the formation heterogeneity and pressure drop caused by wellbore friction. The visualized 2-D sand filling displacement experiment indicates that the injection rate at the horizontal well heel is greater than that at the toe and the injection front is more irregular in heterogeneous formation. The injection rate and injection pressure distribution along the horizontal well are obtained analytically based on the proposed model, the results show that the injection rate at the two sides of the wellbore is much higher than that in the middle when the formation is homogeneous and the wellbore is infinite-conductive. In this case, the injection rate curve along horizontal well shows a "U" shaped distribution. When a finite-conductive horizontal wellbore is considered, the injection rate at the heel of the wellbore is higher than that of the toe, although the injection rate curve along horizontal well also exhibits a deformed "U" shape distribution. For the formation heterogeneities along the horizontal wellbore, the injection rate distribution curve is not continuous anymore, but a deformed "U" shape is also observed for each wellbore segment. At last, the established model was applied to an ultra-heterogeneous offshore reservoir. It is concluded that the profile control effect of typical well is obvious. The results of this study are of great significance for the calculation of the injection rate profile and improving the water injection efficiency.


2021 ◽  
Vol 9 (4B) ◽  
Author(s):  
Bassam A. Albassam ◽  

This paper deals with designing a control force to create nodal point(s) having zero displacement and/or zero slope at selected locations in a vibrating beam structure excited by multiple harmonic forces. It is shown that the steady state vibrations at desired points can be eliminated using applied control forces. The control forces design method is implemented using dynamic Green’s functions that transform the equations of motion from differential to algebraic equations, in which the resulting solution is analytic and exact. The control problem is greatly simplified by utilizing the superposition principle that leads to calculating the control forces to create node(s) for each excitation frequency independently. The calculated control forces can be realized using passive elements such as masses and springs connected to the beam having reaction forces equal to the calculated control forces. The effectiveness of the proposed method is demonstrated on various cases using numerical examples. Through examples, it was shown that creating node(s) with zero deflection, as well as zero slope, not only results in isolated stationary points, but also suppresses the vibrations along a wide region of the beam.


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