The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of pl...The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of plate was constrained by lots of factors. And because the speed was a flexible control parameter,the calculation method of optimal speed profile was developed based on the measured start cooling temperature and its matrix equation was solved by the Cholesky decomposition method. The optimal speed profile was used in online control system. As a result,the temperature distribution along the plate length direction was relatively uniform,and 95% of measured final cooling temperature difference from the target temperature 700 ℃ was controlled within ±20 ℃.展开更多
We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work forc...We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work force, including the force of inertia which obtain equations vibrations of mechanical systems. Frequency equation is solved numerically by the method of Muller. According to the result of numerical analysis we established nonmonotonic dependence damping coefficients of the system parameters.展开更多
The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-ho...The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.展开更多
A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the...A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic viscoelastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs.展开更多
A mathematical model is developed to assist the design engineers by analyzing the vibration response of non-homogeneous orthotropic rectangular plate under exponentially varying thermal condition. Plate thickness vari...A mathematical model is developed to assist the design engineers by analyzing the vibration response of non-homogeneous orthotropic rectangular plate under exponentially varying thermal condition. Plate thickness varies parabolically in both directions. Using Rayleigh Ritz approach, frequency parameter and two term deflection function is calculated for diverse values of taper constants. For the best comprehension of the vibration analysis, results are depicted graphically.展开更多
Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonaliza...Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.展开更多
This model is dedicated to visualizing the nature of magnetite-water nanoliquid induced by a permeable plate having variable magnetic effect,non-linear radiation,heterogeneous and homogeneous chemically reactive spec...This model is dedicated to visualizing the nature of magnetite-water nanoliquid induced by a permeable plate having variable magnetic effect,non-linear radiation,heterogeneous and homogeneous chemically reactive species.The system of momentum,thermal and concentration expressions is formulated and transformed from the partial to ordinary differential systems by using the adequate transforms.This highly non-linear system is solved through RKF(Runge-Kutta-Fehlberg)numerical method.Important parameters such as suction/injection,magnetic,and radiation effects as well as other relevant parameters are investigated.The graphs show that the rise in radiation parameter numerically improves the thermal distribution,implying a faster heat transfer rate.Non-linear radiation has greater effect on temperature than the linear radiation.While the volume concentration effect reveals that the friction factor increase with the enhancement of nanoparticle concentration.It is also observed that,plate velocity decreases the skin-friction but increases the wall heat transfer for both suction and blowing cases.The results indicate that the current research has a strong agreement with the relevant data in a limiting approach.展开更多
文摘The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of plate was constrained by lots of factors. And because the speed was a flexible control parameter,the calculation method of optimal speed profile was developed based on the measured start cooling temperature and its matrix equation was solved by the Cholesky decomposition method. The optimal speed profile was used in online control system. As a result,the temperature distribution along the plate length direction was relatively uniform,and 95% of measured final cooling temperature difference from the target temperature 700 ℃ was controlled within ±20 ℃.
文摘We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work force, including the force of inertia which obtain equations vibrations of mechanical systems. Frequency equation is solved numerically by the method of Muller. According to the result of numerical analysis we established nonmonotonic dependence damping coefficients of the system parameters.
文摘The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.
文摘A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic viscoelastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs.
文摘A mathematical model is developed to assist the design engineers by analyzing the vibration response of non-homogeneous orthotropic rectangular plate under exponentially varying thermal condition. Plate thickness varies parabolically in both directions. Using Rayleigh Ritz approach, frequency parameter and two term deflection function is calculated for diverse values of taper constants. For the best comprehension of the vibration analysis, results are depicted graphically.
文摘Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.
文摘This model is dedicated to visualizing the nature of magnetite-water nanoliquid induced by a permeable plate having variable magnetic effect,non-linear radiation,heterogeneous and homogeneous chemically reactive species.The system of momentum,thermal and concentration expressions is formulated and transformed from the partial to ordinary differential systems by using the adequate transforms.This highly non-linear system is solved through RKF(Runge-Kutta-Fehlberg)numerical method.Important parameters such as suction/injection,magnetic,and radiation effects as well as other relevant parameters are investigated.The graphs show that the rise in radiation parameter numerically improves the thermal distribution,implying a faster heat transfer rate.Non-linear radiation has greater effect on temperature than the linear radiation.While the volume concentration effect reveals that the friction factor increase with the enhancement of nanoparticle concentration.It is also observed that,plate velocity decreases the skin-friction but increases the wall heat transfer for both suction and blowing cases.The results indicate that the current research has a strong agreement with the relevant data in a limiting approach.
基金supported by the Natural Science Foundation of China (10972075,10802029)the Hunan Provincial Natural Science Foundation of China(10JJ3036)Scientific Research Fund of Hunan Provincial Education Depart ment of China(08C230)~~
