Fluid bounding effect on FG cylindrical shell using Hankel's functions of second kind
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- Advances in nano research
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- 제16권6호
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- pp.565-577
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- 2024
Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.
Purpose: Heat transfers phenomena are described by the second order partial differential equation and its boundary conditions. In a three-dimensional structure of a building, the heat transfer phenomena generally include more than one material, and thus, become complicate. The analytic solutions are useful to understand heat transfer phenomena, but they can hardly be applied in engineering or design problems. Engineers and designers have generally been forced to use numerical methods providing reliable results. Finite volume methods with the unstructured grid system is only the suitable means of the analysis for the complex and arbitrary domains. Method: To obtain an numerical solution, a discretization method, which approximates the differential equations, and the interpolation methods for temperature and heat flux between two or more materials are required. The discretization methods are applied to small domains in space and time, and these numerical solutions form the descretized equations provide approximated solutions in both space and time. The accuracy of numerical solutions is dependent on the quality of discretizations and size of cells used. The higher accuracy, the higher numerical resources are required. The balance between the accuracy and difficulty of the numerical methods is critical for the success of the numerical analysis. A simple and easy interpolation methods among multiple materials are developed. The linear equations are solved with the BiCGSTAB being a effective matrix solver. Result: This study provides an overview of discretization methods, boundary interface, and matrix solver for the 3-dimensional numerical heat transfer including two materials.
This paper reports a fundamental study of temperature characteristics of a solar pond with an insulation layer. Further, these characteristics were compared with those of a solar pond without the insulation layer. The governing equation was discretized via finite difference method. The governing equations are two-dimensional unsteady-state second-order partial differential equations. The conclusions of the study are as follows: 1) If the depth of the solar pond was increased, the desired effect of increase in temperature was not produced because the amount of solar insolation received by the bottom of the solar pond decreased. 2) As the temperature of the soil during winter is higher than the temperature of the water in a solar pond, heat was transferred from the soil to the solar pond. 3) For the case of the solar pond with insulation layer, it was estimated that the dependence rate of solar energy was 83.3% and that of the boiler was 16.7%.
The physics-informed neural network (PINN) has been proposed to overcome the limitations of various numerical methods used to solve partial differential equations (PDEs) and the drawbacks of purely data-driven machine learning. The PINN directly applies PDEs to the construction of the loss function, introducing physical constraints to machine learning training. This technique can also be applied to wave equation modeling. However, to solve the wave equation using the PINN, second-order differentiations with respect to input data must be performed during neural network training, and the resulting wavefields contain complex dynamical phenomena, requiring careful strategies. This tutorial elucidates the fundamental concepts of the PINN and discusses considerations for wave equation modeling using the PINN approach. These considerations include spatial coordinate normalization, the selection of activation functions, and strategies for incorporating physics loss. Our experimental results demonstrated that normalizing the spatial coordinates of the training data leads to a more accurate reflection of initial conditions in neural network training for wave equation modeling. Furthermore, the characteristics of various functions were compared to select an appropriate activation function for wavefield prediction using neural networks. These comparisons focused on their differentiation with respect to input data and their convergence properties. Finally, the results of two scenarios for incorporating physics loss into the loss function during neural network training were compared. Through numerical experiments, a curriculum-based learning strategy, applying physics loss after the initial training steps, was more effective than utilizing physics loss from the early training steps. In addition, the effectiveness of the PINN technique was confirmed by comparing these results with those of training without any use of physics loss.
It has been well known and empirically supported that many persons with psychiatric disabilities experience recovery in the community. The sense of recovery is experienced while they recognize and manage mental illness and cope with everyday life utilizing personal and social resources. In order to explore ways in which the sense of recovery is enhanced, this study investigated the structure of relationships among the mental health state, optimism, positive emotions, quantity and quality of the social relationships, coping, and recovery of 460 persons with psychiatric disabilities through structural equation modeling. Of findings, first, in the results of path estimates of measurement and theoretical model, especially optimism and positive emotions demonstrated significant effects on the social relationship, coping, and the recovery, while, by contraries, positive emotions showed no significant direct effects on coping, neither the social relationships did on the recovery. Second, on the recovery optimism and positive emotions had direct effects, while quantity and quality of the social relationships had only indirect effects. It is particularly noted that positive emotions showed stronger effects on the recovery than optimism, and also had direct and indirect effects on the social relationships. Finally, partial mediating effects of coping were found between optimism and the recovery, between quality of the social relationships and recovery, and between quantity and quality of the social relationships; another partial mediating effects of quality of social relationships between quantity of social relationships and coping, and between positive emotions and coping; and the last same effects of quantity of the social relationships between positive emotions and coping. According to these results, discussions and implications for social work practice and practice research were suggested regarding the differential effects of positive cognitions and emotions on the recovery and different mechanisms of the quality and quantity of the social relationships, and the relationships among the resources, coping, and the recovery of persons with psychiatric disabilities.
This study investigated the differential effects of childhood trauma, especially neglect, emotional abuse, and physical abuse on stress perception in relation to the ToM (theory of mind), among one-hundred and fifty five college students. For this purpose, self-reported childhood neglect, emotional abuse, physical abuse, and stress levels during the previous week were measured. Social cognition was measured using a ToM questionnaire which asked respondents to guess the intentions of the person in each vignette by providing additional hints. In order to examine the predicting role of childhood trauma and mediating role of ToM, two distinct structural models assuming full (Model 1) and partial (Model 2) mediational effects were compared using structural equation modeling. The partial mediational model was supported and the main results were as follows. First, childhood neglect indirectly predicted stress perception through the effect of the ToM. Second, childhood emotional abuse directly predicted stress perception. Third, childhood physical abuse had no distinct effect on stress perception. Finally, the limitations of this study and the implications for future studies are discussed.
The wall shear stress in the vicinity of end-to end anastomoses under steady flow conditions was measured using a flush-mounted hot-film anemometer(FMHFA) probe. The experimental measurements were in good agreement with numerical results except in flow with low Reynolds numbers. The wall shear stress increased proximal to the anastomosis in flow from the Penrose tubing (simulating an artery) to the PTFE: graft. In flow from the PTFE graft to the Penrose tubing, low wall shear stress was observed distal to the anastomosis. Abnormal distributions of wall shear stress in the vicinity of the anastomosis, resulting from the compliance mismatch between the graft and the host artery, might be an important factor of ANFH formation and the graft failure. The present study suggests a correlation between regions of the low wall shear stress and the development of anastomotic neointimal fibrous hyperplasia(ANPH) in end-to-end anastomoses. 30523 T00401030523 ^x Air pressure decay(APD) rate and ultrafiltration rate(UFR) tests were performed on new and saline rinsed dialyzers as well as those roused in patients several times. C-DAK 4000 (Cordis Dow) and CF IS-11 (Baxter Travenol) reused dialyzers obtained from the dialysis clinic were used in the present study. The new dialyzers exhibited a relatively flat APD, whereas saline rinsed and reused dialyzers showed considerable amount of decay. C-DAH dialyzers had a larger APD(11.70
The wall shear stress in the vicinity of end-to end anastomoses under steady flow conditions was measured using a flush-mounted hot-film anemometer(FMHFA) probe. The experimental measurements were in good agreement with numerical results except in flow with low Reynolds numbers. The wall shear stress increased proximal to the anastomosis in flow from the Penrose tubing (simulating an artery) to the PTFE: graft. In flow from the PTFE graft to the Penrose tubing, low wall shear stress was observed distal to the anastomosis. Abnormal distributions of wall shear stress in the vicinity of the anastomosis, resulting from the compliance mismatch between the graft and the host artery, might be an important factor of ANFH formation and the graft failure. The present study suggests a correlation between regions of the low wall shear stress and the development of anastomotic neointimal fibrous hyperplasia(ANPH) in end-to-end anastomoses. 30523 T00401030523 ^x Air pressure decay(APD) rate and ultrafiltration rate(UFR) tests were performed on new and saline rinsed dialyzers as well as those roused in patients several times. C-DAK 4000 (Cordis Dow) and CF IS-11 (Baxter Travenol) reused dialyzers obtained from the dialysis clinic were used in the present study. The new dialyzers exhibited a relatively flat APD, whereas saline rinsed and reused dialyzers showed considerable amount of decay. C-DAH dialyzers had a larger APD(11.70