The size of impeller reflux holes for centrifugal pump has influence on the pressure distribution of front and rear shrouds and rear pump chamber, as well as energy characteristics of whole pump and axial force. Low s...The size of impeller reflux holes for centrifugal pump has influence on the pressure distribution of front and rear shrouds and rear pump chamber, as well as energy characteristics of whole pump and axial force. Low specific-speed centrifugal pump with Q=12.5 m3/h, H=60 m, n=2950 r/min was selected to be designed with eight axial reflux balance holes with 4.5 mm in diameter. The simulated Q-H curve and net positive suction head(NPSH) were in good agreement with experimental results, which illustrated that centrifugal pump with axial reflux balance holes was superior in the cavitation characteristic; however, it showed to little superiority in head and efficiency. The pressure in rear pump chamber at 0.6 times rate flow is 29.36% of pressure difference between outlet and inlet, which reduces to 29.10% at rate flow and 28.33% at 1.4 times rate flow. As the whole, the pressure distribution on front and rear shrouds from simulation results is not a standard parabola, and axial force decreases as flow rate increases. Radical reflux balance holes chosen to be 5.2 mm and 5.9 mm in diameter were further designed with other hydraulic parts unchanged. With structural grids adopted for total flow field, contrast numerical simulation on internal flow characteristics was conducted based on momentum equations and standard turbulence model(κ-ε). It is found that axial force of pump with radical reflux balance holes of5.2 mm and 5.9 mm in diameter is significantly less than that with radical reflux balance holes of 4.5 mm in diameter. Better axial force balance is obtained as the ratio of area of reflux balance holes and area of sealing ring exceeds 6.展开更多
The steady axis-symmetrical atmosphere dynamical equations are used for describing spiral structure of tropical cyclones under four-force (pressure gradient force, Coriolis force, centrifugal force, and friction forc...The steady axis-symmetrical atmosphere dynamical equations are used for describing spiral structure of tropical cyclones under four-force (pressure gradient force, Coriolis force, centrifugal force, and friction force) balance, and the dynamical systems of three-dimensional (3D) velocity field are introduced. The qualitative analysis of the dynamical system shows that there are down 3D spiral structures in eye of tropical cyclone and tropical cyclone is 3D counterclockwise up spiral structure. These results are consistent with the observed tropical cyclone on the weather map.展开更多
Cloud dominates influence factors of atmospheric radiation, while aerosol–cloud interactions are of vital importance in its spatiotemporal distribution. In this study, a two-moment(mass and number) cloud microphysics...Cloud dominates influence factors of atmospheric radiation, while aerosol–cloud interactions are of vital importance in its spatiotemporal distribution. In this study, a two-moment(mass and number) cloud microphysics scheme, which significantly improved the treatment of the coupled processes of aerosols and clouds, was incorporated into version 1.1 of the IAP/LASG global Finite-volume Atmospheric Model(FAMIL1.1). For illustrative purposes, the characteristics of the energy balance and cloud radiative forcing(CRF) in an AMIP-type simulation with prescribed aerosols were compared with those in observational/reanalysis data. Even within the constraints of the prescribed aerosol mass, the model simulated global mean energy balance at the top of the atmosphere(TOA) and at the Earth’s surface, as well as their seasonal variation, are in good agreement with the observational data. The maximum deviation terms lie in the surface downwelling longwave radiation and surface latent heat flux, which are 3.5 W m-2(1%) and 3 W m-2(3.5%), individually. The spatial correlations of the annual TOA net radiation flux and the net CRF between simulation and observation were around 0.97 and 0.90, respectively. A major weakness is that FAMIL1.1 predicts more liquid water content and less ice water content over most oceans. Detailed comparisons are presented for a number of regions, with a focus on the Asian monsoon region(AMR). The results indicate that FAMIL1.1 well reproduces the summer–winter contrast for both the geographical distribution of the longwave CRF and shortwave CRF over the AMR. Finally, the model bias and possible solutions, as well as further works to develop FAMIL1.1 are discussed.展开更多
A method of producing rotating radial electromagnetic force with a separable structure is proposed, and an experimental model was designed on which open loop vibration control experiments were carried out. Experimenta...A method of producing rotating radial electromagnetic force with a separable structure is proposed, and an experimental model was designed on which open loop vibration control experiments were carried out. Experimental results prove that the electromagnetic force designed has a constant magnitude and an uniform speed, and the idea of using an electromagnetic force as an active control in automatic balancing is correct in principle, and practicable in engineering.展开更多
Surface nitrogen(N) balances for China's crop production systems were estimated using statistical data collected from 1980 to 2004 at the national and provincial scale and from 1994 to 1999 at the county level.The...Surface nitrogen(N) balances for China's crop production systems were estimated using statistical data collected from 1980 to 2004 at the national and provincial scale and from 1994 to 1999 at the county level.There was a surplus N balance throughout these periods,but the surplus was nearly stable in recent years.Projections using nonseasonal Box-Jenkins model or exponential models show that the N surplus for the total cultivated land in China was likely to increase from 142.8 kg ha?1 in 2004 to 168.6 kg ha-1 in 2015.The N balance surplus in the more developed southeastern provinces was the largest,and was slightly less in the central region,which caused the nitrate pollution in the ground water.The N surplus was much less in the western and northern provinces because of lower synthetic fertilizer inputs.The region with high N risk includes Beijing Municipality and Jiangsu,Zhejiang,Fujian,Guangdong,Hubei,and Shandong provinces for 2002-2004.The projections suggested that 15 provinces(or municipalities) in the middle and southeastern part of China except Jiangxi and Shanxi provinces would become the high-risk region by 2015.The level of economic development,transportation,and labor force condition had an important e?ect on the N balance surplus at the county level,but the last two factors showed remarkable impact at the provincial level.To decrease the nonpoint pollution(Npp) risk from crop production,the authors suggested to reduce the target level for national grain self-suflciency to 90%-95% and change the regional structure of grain production by moving some of the future grain production from the high Npp risk areas of eastern China to parts of the central and western provinces where the Npp risk was much less.展开更多
Starting with a recent unconventional explanation of the lift force on a wing, featuring compressibility of the air, an application of the same concept is made to the lift force on the equatorial sea surface due to th...Starting with a recent unconventional explanation of the lift force on a wing, featuring compressibility of the air, an application of the same concept is made to the lift force on the equatorial sea surface due to the Trade Winds, by greatly increasing the spatial scales. If the equatorial sea level does rise up, the northward slope to the sea level should facilitate the poleward flux of summer heat in both the North Pacific and North Atlantic Oceans, as two examples, in accordance with the heat budget requirements of these oceans. Compressed air dynamics consists of Bernoulli’s law applied to the streamlines of the Trade Winds, the force balance between the upward centrifugal force of the curved streamlines at the earth’s surface and a downward pressure force, and the perfect gas law for air.展开更多
For a single cylinder engine, the total unbalanced inertial forces occur in the engine block, which results in engine’s vibration and deteriorated noise. In order to eliminate the unbalanced forces, counterweight and...For a single cylinder engine, the total unbalanced inertial forces occur in the engine block, which results in engine’s vibration and deteriorated noise. In order to eliminate the unbalanced forces, counterweight and primary balance shaft should be attached to the cylinder block so that engine durability and ride comfortability may be further improved. Traditionally one third of connecting rod assembly’s mass is treated as reciprocating mass, and two thirds as rotating mass when designing balance mechanism. In this paper, a new method based on the multibody dynamics simulation is introduced to separate the reciprocating mass and rotating mass of connecting rod assembly. The model consists of crankshaft, connecting rod, piston and the simulation is performed subsequently. According to the simulation results of the main bearing loads, the reciprocating mass and rotating mass are separated. Finally a new balance mechanism is designed and simulation results show that it completely balances inertial forces to improve the engine’s noise vibration and harshness performance.展开更多
Extraction of a coal seam which lies not far below a heating goaf can be a major safety challenge. A force auxiliary ventilation system was adopted as a control method in successful extraction and recovery of the pane...Extraction of a coal seam which lies not far below a heating goaf can be a major safety challenge. A force auxiliary ventilation system was adopted as a control method in successful extraction and recovery of the panel 30110 of the #3 1coal seam, which is about 30–40 m below the heating goaf of the #2 2seam at Longhua underground coal mine, Shanxi Province, China. Booster fans and ventilation control devices such as doors and regulators were used in the system. The results show that, provided that a force auxiliary ventilation system is properly designed to achieve a pressure balance between a panel and its overlying goaf, the system can be used to extract a coal seam overlain by a heating goaf. This paper describes the design, installation and performance of the ventilation system during the extraction and recovery phases of the panel 30110.展开更多
The dynamic balancing is an important issue in mechanism design. For the existing balancing methods, both passive and active ones, there is still room for improvement in adaplability and independency. In view of this,...The dynamic balancing is an important issue in mechanism design. For the existing balancing methods, both passive and active ones, there is still room for improvement in adaplability and independency. In view of this, a concept of active balancer is developed as a new solution for the dynamic balancing with more flexibility. The proposed balancer is an independent additional device with a control system inside, which consists of a two-degree-of-freedom (DOF) linkage and a controllable motor, and can be attached to a machine expediently with little change to its original structure and motion. One of the two inputs of the two-DOF linkage shares the same shaft with its output, which is connected to the input shaft of a machine to be balanced and driven by the original actuator. The other input is driven by the control motor. By properly selecting the speed trajectories of the control motor and link parameters of the two-DOF linkage, one or more dynamic effects of the mechanisms can be minimized or eliminated adaptively. The design procedure of the active balancer is put forward and a two-step optimization is developed to find out optimal design parameters of the balancer for various design requirements and constraints. Taking a force-balanced crank-rocker mechanism as the reference mechanism, numerical examples are given to illustrate the design procedure. The balancing effects of the proposed balancer are compared with those of the existing adding dyads (DYAD) method. The results show that the introduction of the control system provides the active balancer with better balancing effect and more flexibility than the DYAD method. A considerable reduction in the dynamic effects (input torque, shaking moment and shaking force) can be achieved for different balancing object by designing the structural and control parameters of the balancer, and the deterioration of dynamic performance caused by alterative working conditions can be compensated effectively by redesigning the control parameters.展开更多
The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of dif- ferent analytical approximate approaches. The forced vibra...The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of dif- ferent analytical approximate approaches. The forced vibration of snap-through mecha- nism is treated as a quadratic nonlinear oscillator. The Lindstedt-Poincar method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses. It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method. The analytical approximations are com- pared with the numerical integrations in terms of the frequency response curves and the phase portraits. Supported by the numerical results, the harmonic balance method pre- dicts that the quadratic nonlinearity bends the frequency response curves to the left. If the excitation amplitude is a second-order small quantity of the bookkeeping parameter, the steady-state responses predicted by the second-order approximation of the Lindstedt- Poincar method and the multiple-scale method agree qualitatively with the numerical results. It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.展开更多
We analyze the familiar effect of the pulling of a magnetizable rod by a magnetic field inside a solenoid. We find that the analogy with the pulling of a dielectric slab by a charged capacitor is not as direct as usua...We analyze the familiar effect of the pulling of a magnetizable rod by a magnetic field inside a solenoid. We find that the analogy with the pulling of a dielectric slab by a charged capacitor is not as direct as usually thought. Indeed, there are two possibilities to pursue the analogy, according to the correspondence used,?either E → B and D → H, or E?→ H and D?→ B. One of these results in an incorrect sign in the force, while the other gives the correct result. We avoid this ambiguity in the usual energy method applying a momentum balance equation derived from Maxwell’s equations. This method permits the calculation of the force with a volume integration of a force density, or with a surface integration of a stress tensor. An interpretation of our results establishes that the force acts at the interface and has its origin in Maxwell′s magnetic stresses at the medium-vacuum interface. This approach provides new insights and a new perspective of the origin of this force.展开更多
We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic f...We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic functions are used instead of circular trigonometric functions. We show that a simple change of independent variable followed by a careful choice of the form of anharmonic solution enable to obtain highly accurate approximate solutions. In particular our examples show that the proposed method is as easy to use as existing harmonic balance based methods and yet provides substantially greater accuracy.展开更多
With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these ...With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these forces are not exactly analogous, as usually thought. We present a device that is a proper analogy of the case of a dielectric slab inside a capacitor. Our analysis shows the significance of the electrostatic and magnetostatic pressures to the understanding of these effects and shows the conceptual differences between both cases.展开更多
Balance valve is a core component of the 11000-meter manned submersible“struggle,”and its sealing performance is crucial and challenging when the maximum pressure difference is 118 MPa.The increasing sealing force i...Balance valve is a core component of the 11000-meter manned submersible“struggle,”and its sealing performance is crucial and challenging when the maximum pressure difference is 118 MPa.The increasing sealing force improves the sealing performance and increases the system’s energy consumption at the same time.A hybrid analytical–numerical–experimental(ANE)model is proposed to obtain the minimum sealing force,ensuring no leakage at the valve port and reducing energy consumption as much as possible.The effects of roundness error,environmental pressure,and materials on the minimum sealing force are considered in the ANE model.The basic form of minimum sealing force equations is established,and the remaining unknown coefficients of the equations are obtained by the finite element method(FEM).The accuracy of the equation is evaluated by comparing the independent FEM data to the equation data.Results of the comparison show good agreement,and the difference between the independent FEM data and equation data is within 3%when the environmental pressure is 0–118 MPa.Finally,the minimum sealing force equation is applied in a balance valve to be experimented using a deep-sea simulation device.The balance valve designed through the minimum sealing force equation is leak-free in the experiment.Thus,the minimum sealing force equation is suitable for the ultrahigh pressure balance valve and has guiding significance for evaluating the sealing performance of ultrahigh pressure balance valves.展开更多
基金Project(51179075)supported by the National Natural Science Foundation of ChinaProject(BK20131256)supported by the Natural Science Funds of Jiangsu Province,ChinaProject supported by the Priority Academic Program Development of Jiangsu High Education Institutions,China
文摘The size of impeller reflux holes for centrifugal pump has influence on the pressure distribution of front and rear shrouds and rear pump chamber, as well as energy characteristics of whole pump and axial force. Low specific-speed centrifugal pump with Q=12.5 m3/h, H=60 m, n=2950 r/min was selected to be designed with eight axial reflux balance holes with 4.5 mm in diameter. The simulated Q-H curve and net positive suction head(NPSH) were in good agreement with experimental results, which illustrated that centrifugal pump with axial reflux balance holes was superior in the cavitation characteristic; however, it showed to little superiority in head and efficiency. The pressure in rear pump chamber at 0.6 times rate flow is 29.36% of pressure difference between outlet and inlet, which reduces to 29.10% at rate flow and 28.33% at 1.4 times rate flow. As the whole, the pressure distribution on front and rear shrouds from simulation results is not a standard parabola, and axial force decreases as flow rate increases. Radical reflux balance holes chosen to be 5.2 mm and 5.9 mm in diameter were further designed with other hydraulic parts unchanged. With structural grids adopted for total flow field, contrast numerical simulation on internal flow characteristics was conducted based on momentum equations and standard turbulence model(κ-ε). It is found that axial force of pump with radical reflux balance holes of5.2 mm and 5.9 mm in diameter is significantly less than that with radical reflux balance holes of 4.5 mm in diameter. Better axial force balance is obtained as the ratio of area of reflux balance holes and area of sealing ring exceeds 6.
基金supported by the National Natural Science Foundation of China(Granted No.40975027)
文摘The steady axis-symmetrical atmosphere dynamical equations are used for describing spiral structure of tropical cyclones under four-force (pressure gradient force, Coriolis force, centrifugal force, and friction force) balance, and the dynamical systems of three-dimensional (3D) velocity field are introduced. The qualitative analysis of the dynamical system shows that there are down 3D spiral structures in eye of tropical cyclone and tropical cyclone is 3D counterclockwise up spiral structure. These results are consistent with the observed tropical cyclone on the weather map.
基金funded by the National Natural Science Foundation of China (Grants 41675100, 91737306, and U1811464)
文摘Cloud dominates influence factors of atmospheric radiation, while aerosol–cloud interactions are of vital importance in its spatiotemporal distribution. In this study, a two-moment(mass and number) cloud microphysics scheme, which significantly improved the treatment of the coupled processes of aerosols and clouds, was incorporated into version 1.1 of the IAP/LASG global Finite-volume Atmospheric Model(FAMIL1.1). For illustrative purposes, the characteristics of the energy balance and cloud radiative forcing(CRF) in an AMIP-type simulation with prescribed aerosols were compared with those in observational/reanalysis data. Even within the constraints of the prescribed aerosol mass, the model simulated global mean energy balance at the top of the atmosphere(TOA) and at the Earth’s surface, as well as their seasonal variation, are in good agreement with the observational data. The maximum deviation terms lie in the surface downwelling longwave radiation and surface latent heat flux, which are 3.5 W m-2(1%) and 3 W m-2(3.5%), individually. The spatial correlations of the annual TOA net radiation flux and the net CRF between simulation and observation were around 0.97 and 0.90, respectively. A major weakness is that FAMIL1.1 predicts more liquid water content and less ice water content over most oceans. Detailed comparisons are presented for a number of regions, with a focus on the Asian monsoon region(AMR). The results indicate that FAMIL1.1 well reproduces the summer–winter contrast for both the geographical distribution of the longwave CRF and shortwave CRF over the AMR. Finally, the model bias and possible solutions, as well as further works to develop FAMIL1.1 are discussed.
文摘A method of producing rotating radial electromagnetic force with a separable structure is proposed, and an experimental model was designed on which open loop vibration control experiments were carried out. Experimental results prove that the electromagnetic force designed has a constant magnitude and an uniform speed, and the idea of using an electromagnetic force as an active control in automatic balancing is correct in principle, and practicable in engineering.
基金the Chinese Academy of Sciences (NoKZCX2-YW-N-038)the National Basic Research Program of China (No2005CB121108)
文摘Surface nitrogen(N) balances for China's crop production systems were estimated using statistical data collected from 1980 to 2004 at the national and provincial scale and from 1994 to 1999 at the county level.There was a surplus N balance throughout these periods,but the surplus was nearly stable in recent years.Projections using nonseasonal Box-Jenkins model or exponential models show that the N surplus for the total cultivated land in China was likely to increase from 142.8 kg ha?1 in 2004 to 168.6 kg ha-1 in 2015.The N balance surplus in the more developed southeastern provinces was the largest,and was slightly less in the central region,which caused the nitrate pollution in the ground water.The N surplus was much less in the western and northern provinces because of lower synthetic fertilizer inputs.The region with high N risk includes Beijing Municipality and Jiangsu,Zhejiang,Fujian,Guangdong,Hubei,and Shandong provinces for 2002-2004.The projections suggested that 15 provinces(or municipalities) in the middle and southeastern part of China except Jiangxi and Shanxi provinces would become the high-risk region by 2015.The level of economic development,transportation,and labor force condition had an important e?ect on the N balance surplus at the county level,but the last two factors showed remarkable impact at the provincial level.To decrease the nonpoint pollution(Npp) risk from crop production,the authors suggested to reduce the target level for national grain self-suflciency to 90%-95% and change the regional structure of grain production by moving some of the future grain production from the high Npp risk areas of eastern China to parts of the central and western provinces where the Npp risk was much less.
文摘Starting with a recent unconventional explanation of the lift force on a wing, featuring compressibility of the air, an application of the same concept is made to the lift force on the equatorial sea surface due to the Trade Winds, by greatly increasing the spatial scales. If the equatorial sea level does rise up, the northward slope to the sea level should facilitate the poleward flux of summer heat in both the North Pacific and North Atlantic Oceans, as two examples, in accordance with the heat budget requirements of these oceans. Compressed air dynamics consists of Bernoulli’s law applied to the streamlines of the Trade Winds, the force balance between the upward centrifugal force of the curved streamlines at the earth’s surface and a downward pressure force, and the perfect gas law for air.
基金Supported by National Natural Science Foundation of China (No50575203)
文摘For a single cylinder engine, the total unbalanced inertial forces occur in the engine block, which results in engine’s vibration and deteriorated noise. In order to eliminate the unbalanced forces, counterweight and primary balance shaft should be attached to the cylinder block so that engine durability and ride comfortability may be further improved. Traditionally one third of connecting rod assembly’s mass is treated as reciprocating mass, and two thirds as rotating mass when designing balance mechanism. In this paper, a new method based on the multibody dynamics simulation is introduced to separate the reciprocating mass and rotating mass of connecting rod assembly. The model consists of crankshaft, connecting rod, piston and the simulation is performed subsequently. According to the simulation results of the main bearing loads, the reciprocating mass and rotating mass are separated. Finally a new balance mechanism is designed and simulation results show that it completely balances inertial forces to improve the engine’s noise vibration and harshness performance.
基金supported by the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents and Science Research Innovative Group of Resources and Environment Engineering College of Shandong University of Science and Technology (No. 2012ZHTD06)the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No. 2013RCJJ049)+1 种基金the China Postdoctoral Science Foundation (No. 2013M541942)the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20133718120013)
文摘Extraction of a coal seam which lies not far below a heating goaf can be a major safety challenge. A force auxiliary ventilation system was adopted as a control method in successful extraction and recovery of the panel 30110 of the #3 1coal seam, which is about 30–40 m below the heating goaf of the #2 2seam at Longhua underground coal mine, Shanxi Province, China. Booster fans and ventilation control devices such as doors and regulators were used in the system. The results show that, provided that a force auxiliary ventilation system is properly designed to achieve a pressure balance between a panel and its overlying goaf, the system can be used to extract a coal seam overlain by a heating goaf. This paper describes the design, installation and performance of the ventilation system during the extraction and recovery phases of the panel 30110.
基金supported by National Natural Science Foundation of China (Grant No. 50405004, 50875018)Key Project of National Natural Science Foundation of China (Grant No.50335040)
文摘The dynamic balancing is an important issue in mechanism design. For the existing balancing methods, both passive and active ones, there is still room for improvement in adaplability and independency. In view of this, a concept of active balancer is developed as a new solution for the dynamic balancing with more flexibility. The proposed balancer is an independent additional device with a control system inside, which consists of a two-degree-of-freedom (DOF) linkage and a controllable motor, and can be attached to a machine expediently with little change to its original structure and motion. One of the two inputs of the two-DOF linkage shares the same shaft with its output, which is connected to the input shaft of a machine to be balanced and driven by the original actuator. The other input is driven by the control motor. By properly selecting the speed trajectories of the control motor and link parameters of the two-DOF linkage, one or more dynamic effects of the mechanisms can be minimized or eliminated adaptively. The design procedure of the active balancer is put forward and a two-step optimization is developed to find out optimal design parameters of the balancer for various design requirements and constraints. Taking a force-balanced crank-rocker mechanism as the reference mechanism, numerical examples are given to illustrate the design procedure. The balancing effects of the proposed balancer are compared with those of the existing adding dyads (DYAD) method. The results show that the introduction of the control system provides the active balancer with better balancing effect and more flexibility than the DYAD method. A considerable reduction in the dynamic effects (input torque, shaking moment and shaking force) can be achieved for different balancing object by designing the structural and control parameters of the balancer, and the deterioration of dynamic performance caused by alterative working conditions can be compensated effectively by redesigning the control parameters.
基金Project supported by the State Key Program of National Natural Science Foundation of China(No.11232009)the National Natural Science Foundation of China(No.11572182)
文摘The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of dif- ferent analytical approximate approaches. The forced vibration of snap-through mecha- nism is treated as a quadratic nonlinear oscillator. The Lindstedt-Poincar method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses. It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method. The analytical approximations are com- pared with the numerical integrations in terms of the frequency response curves and the phase portraits. Supported by the numerical results, the harmonic balance method pre- dicts that the quadratic nonlinearity bends the frequency response curves to the left. If the excitation amplitude is a second-order small quantity of the bookkeeping parameter, the steady-state responses predicted by the second-order approximation of the Lindstedt- Poincar method and the multiple-scale method agree qualitatively with the numerical results. It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.
文摘We analyze the familiar effect of the pulling of a magnetizable rod by a magnetic field inside a solenoid. We find that the analogy with the pulling of a dielectric slab by a charged capacitor is not as direct as usually thought. Indeed, there are two possibilities to pursue the analogy, according to the correspondence used,?either E → B and D → H, or E?→ H and D?→ B. One of these results in an incorrect sign in the force, while the other gives the correct result. We avoid this ambiguity in the usual energy method applying a momentum balance equation derived from Maxwell’s equations. This method permits the calculation of the force with a volume integration of a force density, or with a surface integration of a stress tensor. An interpretation of our results establishes that the force acts at the interface and has its origin in Maxwell′s magnetic stresses at the medium-vacuum interface. This approach provides new insights and a new perspective of the origin of this force.
文摘We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic functions are used instead of circular trigonometric functions. We show that a simple change of independent variable followed by a careful choice of the form of anharmonic solution enable to obtain highly accurate approximate solutions. In particular our examples show that the proposed method is as easy to use as existing harmonic balance based methods and yet provides substantially greater accuracy.
文摘With the insight provided by a balance equation of electromagnetic momentum, we compare the force on a dielectric slab inside a capacitor with the force on a magnetizable rod inside a solenoid. We conclude that these forces are not exactly analogous, as usually thought. We present a device that is a proper analogy of the case of a dielectric slab inside a capacitor. Our analysis shows the significance of the electrostatic and magnetostatic pressures to the understanding of these effects and shows the conceptual differences between both cases.
基金National Natural Science Foundation of China (Grant Nos.52122502,51879114,and 52075192).
文摘Balance valve is a core component of the 11000-meter manned submersible“struggle,”and its sealing performance is crucial and challenging when the maximum pressure difference is 118 MPa.The increasing sealing force improves the sealing performance and increases the system’s energy consumption at the same time.A hybrid analytical–numerical–experimental(ANE)model is proposed to obtain the minimum sealing force,ensuring no leakage at the valve port and reducing energy consumption as much as possible.The effects of roundness error,environmental pressure,and materials on the minimum sealing force are considered in the ANE model.The basic form of minimum sealing force equations is established,and the remaining unknown coefficients of the equations are obtained by the finite element method(FEM).The accuracy of the equation is evaluated by comparing the independent FEM data to the equation data.Results of the comparison show good agreement,and the difference between the independent FEM data and equation data is within 3%when the environmental pressure is 0–118 MPa.Finally,the minimum sealing force equation is applied in a balance valve to be experimented using a deep-sea simulation device.The balance valve designed through the minimum sealing force equation is leak-free in the experiment.Thus,the minimum sealing force equation is suitable for the ultrahigh pressure balance valve and has guiding significance for evaluating the sealing performance of ultrahigh pressure balance valves.