This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave fo...This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.展开更多
The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a ...The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.展开更多
In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz ...In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz equation was used as a governing equation.The boundary element method（BEM） was adopted to discretize the relevant equations.Open boundaries were used in far fields of the study domain.Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them.Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders,ka and kd on forces and trapped modes.The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data.The comparisons confirm the accuracy of the model.The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders.Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0.Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.展开更多
-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection char...-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the...So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.展开更多
Schrödinger equations are very common equations in physics and mathematics for nonlinear physics to model the dynamics of wave propagation in waveguides such as power lines, atomic chains, optical fibers, and eve...Schrödinger equations are very common equations in physics and mathematics for nonlinear physics to model the dynamics of wave propagation in waveguides such as power lines, atomic chains, optical fibers, and even in quantum mechanics. But all these equations are most often studied without worrying about what would happen if this equation were maintained, that is to say, had a second member synonymous with an external force. It is true that on a physical level, such equations can be considered as describing the generation of waves on a waveguide using an external force. However, the in-depth analysis of this aspect is not at the center of our reflection in this article, but for us, it is a question of proposing exact solutions to this type of equation and above all proposing the general form of the external force so that the obtaining exact solutions is possible.展开更多
A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exteri...A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.展开更多
The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has...The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.展开更多
Based on the covariant Lagrangian function and Euler-Lagrange equation,a set of classical fluid equations for strong EM wave-spin plasma interaction is derived.Analysis shows that the relativistic effects may affect t...Based on the covariant Lagrangian function and Euler-Lagrange equation,a set of classical fluid equations for strong EM wave-spin plasma interaction is derived.Analysis shows that the relativistic effects may affect the interaction processes by three factors:the relativistic factor,the time component of four-spin,and the velocity-field coupling.This set of equations can be used to discuss the collective spin effects of relativistic electrons in classical regime,such as astrophysics,high-energy laser-plasma systems and so on.As an example,the spin induced ponderomotive force in the interaction of strong EM wave and magnetized plasma is investigated.Results show that the time component of four-spin,which approaches to zero in nonrelativistic situations,can increase the spin-ponderomotive force obviously in relativistic situation.展开更多
It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in t...It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.展开更多
V_(1)导联P波终末电势(P-wave terminal force in V_(1),PtfV_(1))又称Morris指数,在心房颤动(简称房颤)相关脑卒中风险评估方面有着举足轻重的作用。PtfV_(1)与急性缺血性脑卒中、急性心肌梗死后的新发房颤、冠状动脉病变、心力衰竭、...V_(1)导联P波终末电势(P-wave terminal force in V_(1),PtfV_(1))又称Morris指数,在心房颤动(简称房颤)相关脑卒中风险评估方面有着举足轻重的作用。PtfV_(1)与急性缺血性脑卒中、急性心肌梗死后的新发房颤、冠状动脉病变、心力衰竭、左心室舒张功能障碍、睡眠呼吸障碍、急性精神压力、弥漫性大B细胞淋巴瘤等疾病的诊断和预后预测也有一定相关性。本文主要综述PtfV_(1)应用于多种临床疾病诊断及预后预测的最新研究进展。展开更多
基金supported by the National Natural Science Foundation of China(Nos.51239008 and 51279130)
文摘This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.
基金funded by the National Natural Science Foundation of China(No.51809135)the Shandong Provincial Natural Science Foundation(No.ZR2018BEE 047)+1 种基金the National Natural Science Foundation of China–Shandong Joint Fund(No.U2006229)the SKL of HESS(No.HESS-1808).
文摘The selection of wave force models will significantly impact the structural responses of floating wind turbines.In this study,comparisons of wave force model effects on the structural responses and fatigue loads of a semi-submersible floating wind turbine(SFWT)were conducted.Simulations were performed by employing the Morison equation(ME)with linear or second-order wave kinematics and potential flow theory(PFT)with first-or second-order wave forces.A comparison of regular waves,irregular waves,and coupled wind/waves analyses with the experimental data showed that many of the simulation results and experimental data are relatively consistent.However,notable discrepancies are found in the response amplitude operators for platform heave,tower base bending moment,and tension in mooring lines.PFT models give more satisfactory results of heave but more significant discrepan-cies in tower base bending moment than the ME models.In irregular wave analyses,low-frequency resonances were captured by PFT models with second-order difference-frequency terms,and high-frequency resonances were captured by the ME models or PFT models with second-order sum-frequency terms.These force models capture the response frequencies but do not reasonably predict the response amplitudes.The coupled wind/waves analyses showed more satisfactory results than the wave-only analyses.However,an important detail to note is that this satisfactory result is based on the overprediction of wind-induced responses.
文摘In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders.The fluid was considered to be inviscid and irrotational.Therefore,the Helmholtz equation was used as a governing equation.The boundary element method（BEM） was adopted to discretize the relevant equations.Open boundaries were used in far fields of the study domain.Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them.Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders,ka and kd on forces and trapped modes.The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data.The comparisons confirm the accuracy of the model.The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders.Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0.Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.
文摘-In this paper, an analytical solution in the outer region of finite water depth is derived for the second-order diffraction potential, which gives a clear physical meaning of the wave transmission and reflection characteristics in the far field. A numerical method-simple Green's function technique-for calculating the second-order diffraction potential in the inner region is also described. Numerical results are provided for the second-order wave forces on a semi-submerged cylinder. It is found that the contribution of second-order diffraction potential to second-order wave forces is important. The effect of water depth and submerged depth on the wave force is also discussed.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
文摘So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.
文摘Schrödinger equations are very common equations in physics and mathematics for nonlinear physics to model the dynamics of wave propagation in waveguides such as power lines, atomic chains, optical fibers, and even in quantum mechanics. But all these equations are most often studied without worrying about what would happen if this equation were maintained, that is to say, had a second member synonymous with an external force. It is true that on a physical level, such equations can be considered as describing the generation of waves on a waveguide using an external force. However, the in-depth analysis of this aspect is not at the center of our reflection in this article, but for us, it is a question of proposing exact solutions to this type of equation and above all proposing the general form of the external force so that the obtaining exact solutions is possible.
文摘A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column.The fluid domain is divided into interior and exterior regions.In the exterior region,the second-order velocity potential is expressed in terms of‘locked-wave’and‘free-wave’ components,both are solved using Fourier and eigenfunction expansions.The re- sulting‘locked wave’potential is expressed by one-dimensional Green's integrals with oscillating integrands.In order to increase computational efficiency,the far-field part of the integrals are carried out analytically.Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions.Based on the present approach,the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates the incident wave spectrum with second-order forcing spectrum on the column.The sum-frequency QTFs for a TLP column are present,which are compared for some frequency pairs with those from a fully numerical procedure.Satisfactory agreement has been obtained.QTF spectra for a case study TLP column,generated using the semi-analytical solution are presented.Also given are the results for nonlinear wave field around the column.
文摘The phenomenon of electrical attraction and repulsion between charged particles is well known, and described mathematically by Coulomb’s Law, yet until now there has been no explanation for why this occurs. There has been no mechanistic explanation that reveals what causes the charged particles to accelerate, either towards or away from each other. This paper gives a detailed explanation of the phenomena of electrical attraction and repulsion based on my previous work that determined the exact wave-function solutions for both the Electron and the Positron. It is revealed that the effects are caused by wave interactions between the wave functions that result in Electromagnetic reflections of parts of the particle’s wave functions, causing a change in their momenta.
基金supported by National Natural Science Foundation of China(No.12065011)Science and Technology Research Project of Jiangxi Provincial Department of Education(No.GJJ170642)。
文摘Based on the covariant Lagrangian function and Euler-Lagrange equation,a set of classical fluid equations for strong EM wave-spin plasma interaction is derived.Analysis shows that the relativistic effects may affect the interaction processes by three factors:the relativistic factor,the time component of four-spin,and the velocity-field coupling.This set of equations can be used to discuss the collective spin effects of relativistic electrons in classical regime,such as astrophysics,high-energy laser-plasma systems and so on.As an example,the spin induced ponderomotive force in the interaction of strong EM wave and magnetized plasma is investigated.Results show that the time component of four-spin,which approaches to zero in nonrelativistic situations,can increase the spin-ponderomotive force obviously in relativistic situation.
文摘It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.
文摘V_(1)导联P波终末电势(P-wave terminal force in V_(1),PtfV_(1))又称Morris指数,在心房颤动(简称房颤)相关脑卒中风险评估方面有着举足轻重的作用。PtfV_(1)与急性缺血性脑卒中、急性心肌梗死后的新发房颤、冠状动脉病变、心力衰竭、左心室舒张功能障碍、睡眠呼吸障碍、急性精神压力、弥漫性大B细胞淋巴瘤等疾病的诊断和预后预测也有一定相关性。本文主要综述PtfV_(1)应用于多种临床疾病诊断及预后预测的最新研究进展。
