Global warming has led to major melting of ice in the polar Arctic,making it possible to open Arctic shipping lanes.In this case,the large number of ice sheets are extremely dangerous for ship navigation,so in this pa...Global warming has led to major melting of ice in the polar Arctic,making it possible to open Arctic shipping lanes.In this case,the large number of ice sheets are extremely dangerous for ship navigation,so in this paper,a body floating on water confined between two finite ice sheets is investigated.The linearized potential flow theory is adopted,and water is considered an incompressible ideal fluid with a finite depth of the fluid domain.The ice sheets are treated as elastic plates,and the problem is solved by matching eigenfunction expansion.The fluid domain is divided into subregions on the basis of the water surface conditions,and the velocity potential of the subdomains is expanded via the separated variable method.By utilizing the continuity of pressure and velocity at the interfaces of two neighboring regions,a system of linear equations is established to obtain the unknown coefficients in the expansion,which in turn leads to analytical solutions for different motion modes in different regions.The effects of different structural drafts,and different lengths of ice sheets on both sides,etc.,on the hydrodynamic characteristics of floats are analyzed.The amplitude of motion of the float is explored,as is the wave elevation between the ice sheets and the float.展开更多
On the basis of a potential theory and Euler-Bernoulli beam theory, an analytical solution for oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography is developed usin...On the basis of a potential theory and Euler-Bernoulli beam theory, an analytical solution for oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography is developed using matched eigenfunction expansions. Different from previous studies, the effects of a wave incident angle, a plate draft, three different plate edge conditions （free, simply supported and built-in） and a sea-bottom topography are all taken into account. Moreover, the plate edge conditions are directly incorporated into linear algebraic equations for determining unknown expansion coefficients in velocity potentials, which leads to a simple and efficient solving procedure. Numerical results show that the convergence of the present solution is good, and an energy conservation relation is well satisfied. Also, the present predictions are in good agreement with known results for special cases. The effects of the wave incident angle, the plate draft, the plate edge conditions and the sea-bottom topography on various hydrodynamic quantities are analyzed. Some useful results are presented for engineering designs.展开更多
The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interf...The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.展开更多
The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral str...The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.展开更多
This study examines wave reflection by a multi-chamber partially perforated caisson breakwater based on potential theory.A quadratic pressure drop boundary condition at perforated walls is adopted,which can well consi...This study examines wave reflection by a multi-chamber partially perforated caisson breakwater based on potential theory.A quadratic pressure drop boundary condition at perforated walls is adopted,which can well consider the effect of wave height on the wave dissipation by perforated walls.The matched eigenfunction expansions with iterative calculations are applied to develop an analytical solution for the present problem.The convergences of both the iterative calculations and the series solution itself are confirmed to be satisfactory.The calculation results of the present analytical solution are in excellent agreement with the numerical results of a multi-domain boundary element solution.Also,the predictions by the present solution are in reasonable agreement with experimental data in literature.Major factors that affect the reflection coefficient of the perforated caisson breakwater are examined by calculation examples.The analysis results show that the multi-chamber perforated caisson breakwater has a better wave energy dissipation function(lower reflection coefficient)than the single-chamber type over a broad range of wave frequency and may perform better if the perforated walls have larger porosities.When the porosities of the perforated walls decrease along the incident wave direction,the perforated caisson breakwater can achieve a lower reflection coefficient.The present analytical solution is simple and reliable,and it can be used as an efficient tool for analyzing the hydrodynamic performance of perforated breakwaters in preliminary engineering design.展开更多
An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear...An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow.Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system.According to the surface boundary conditions,the fluid domain is divided into two regions,namely,an open water region and a plate-covered region.With the assumption that all the motion is time-harmonic,the series solutions for the spatial velocity potentials are derived by the method of eigenfunction expansion.The matching conditions for the continuities of the velocity and pressure are transformed by taking the inner products successively with respect to the vertical eigenfunction for the free surface and the angular eigenfunction.A system of simultaneous equations,including two edge conditions and two matching conditions,is set up for deriving the expansion coefficients.As an example,numerical computation for the expansion coefficients of truncated series is performed for an elliptic plate.The results show that the method suggested here is useful to revealing the physical features of the gravity wave scattering in the open water and the hydroelastic response in the plate.展开更多
A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory...A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.展开更多
文摘Global warming has led to major melting of ice in the polar Arctic,making it possible to open Arctic shipping lanes.In this case,the large number of ice sheets are extremely dangerous for ship navigation,so in this paper,a body floating on water confined between two finite ice sheets is investigated.The linearized potential flow theory is adopted,and water is considered an incompressible ideal fluid with a finite depth of the fluid domain.The ice sheets are treated as elastic plates,and the problem is solved by matching eigenfunction expansion.The fluid domain is divided into subregions on the basis of the water surface conditions,and the velocity potential of the subdomains is expanded via the separated variable method.By utilizing the continuity of pressure and velocity at the interfaces of two neighboring regions,a system of linear equations is established to obtain the unknown coefficients in the expansion,which in turn leads to analytical solutions for different motion modes in different regions.The effects of different structural drafts,and different lengths of ice sheets on both sides,etc.,on the hydrodynamic characteristics of floats are analyzed.The amplitude of motion of the float is explored,as is the wave elevation between the ice sheets and the float.
基金The National Natural Science Foundation of China under contract Nos 51490675,51322903 and 51279224
文摘On the basis of a potential theory and Euler-Bernoulli beam theory, an analytical solution for oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography is developed using matched eigenfunction expansions. Different from previous studies, the effects of a wave incident angle, a plate draft, three different plate edge conditions （free, simply supported and built-in） and a sea-bottom topography are all taken into account. Moreover, the plate edge conditions are directly incorporated into linear algebraic equations for determining unknown expansion coefficients in velocity potentials, which leads to a simple and efficient solving procedure. Numerical results show that the convergence of the present solution is good, and an energy conservation relation is well satisfied. Also, the present predictions are in good agreement with known results for special cases. The effects of the wave incident angle, the plate draft, the plate edge conditions and the sea-bottom topography on various hydrodynamic quantities are analyzed. Some useful results are presented for engineering designs.
基金sponsored by the National Basic Research Program of China(973 Program,Grant No.2014CB046203)the National Natural Science Foundation of China(Grant No.11072140)
文摘The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.
基金Project supported by the National Basic Research Program of China(973 Programm)(No.2014CB046203)the National Natural Science Foundation of China(No.11472166)the Natural Science Foundation of Shanghai(No.14ZR1416200)
文摘The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.
基金The National Natural Science Foundation of China under contract Nos 51725903 and 51490675。
文摘This study examines wave reflection by a multi-chamber partially perforated caisson breakwater based on potential theory.A quadratic pressure drop boundary condition at perforated walls is adopted,which can well consider the effect of wave height on the wave dissipation by perforated walls.The matched eigenfunction expansions with iterative calculations are applied to develop an analytical solution for the present problem.The convergences of both the iterative calculations and the series solution itself are confirmed to be satisfactory.The calculation results of the present analytical solution are in excellent agreement with the numerical results of a multi-domain boundary element solution.Also,the predictions by the present solution are in reasonable agreement with experimental data in literature.Major factors that affect the reflection coefficient of the perforated caisson breakwater are examined by calculation examples.The analysis results show that the multi-chamber perforated caisson breakwater has a better wave energy dissipation function(lower reflection coefficient)than the single-chamber type over a broad range of wave frequency and may perform better if the perforated walls have larger porosities.When the porosities of the perforated walls decrease along the incident wave direction,the perforated caisson breakwater can achieve a lower reflection coefficient.The present analytical solution is simple and reliable,and it can be used as an efficient tool for analyzing the hydrodynamic performance of perforated breakwaters in preliminary engineering design.
基金supported by the National Natural Science Foundation of China (Grant No. 11072140)the State Key Laboratory of Ocean Engineering (Shanghai Jiao Tong University) (Grant No. 0803)+1 种基金the Innovation Program of Shanghai Municipal Education Commission (Grant No.09YZ04)The Shanghai Program for Innovative Research Team in Universities is also acknowledged
文摘An analytical method is developed for the hydroelastic interaction between surface incident waves and a thin elastic plate of arbitrary geometry floating on an inviscid fluid of finite depth in the framework of linear potential flow.Three kinds of edge conditions are considered and the corresponding analytical representations are derived in the polar coordinate system.According to the surface boundary conditions,the fluid domain is divided into two regions,namely,an open water region and a plate-covered region.With the assumption that all the motion is time-harmonic,the series solutions for the spatial velocity potentials are derived by the method of eigenfunction expansion.The matching conditions for the continuities of the velocity and pressure are transformed by taking the inner products successively with respect to the vertical eigenfunction for the free surface and the angular eigenfunction.A system of simultaneous equations,including two edge conditions and two matching conditions,is set up for deriving the expansion coefficients.As an example,numerical computation for the expansion coefficients of truncated series is performed for an elliptic plate.The results show that the method suggested here is useful to revealing the physical features of the gravity wave scattering in the open water and the hydroelastic response in the plate.
基金Project supported by the Ministry of Industry and Information Technology(MIIT)with the Research Project in the Fields of High-Technology Ships(Grant Nos.[2016]22,[2016]548)the National Natural Science Foundation of China(Grant No.11472166)the Natural Science Foundation of Jiangsu Province(Grant No.BK20130109)
文摘A research of wave propagation over a two-layer porous barrier, each layer of which is with different values of porosity and friction, is conducted with a theoretical model in the frame of linear potential flow theory. The model is more appropriate when the seabed consists of two different properties, such as rocks and breakwaters. It is assumed that the fluid is inviscid and incompressible and the motion is irrotational. The wave numbers in the porous region are complex ones, which are related to the decaying and propagating behaviors of wave modes. With the aid of the eigenfunction expansions, a new inner product of the eigenfunctions in the two-layer porous region is proposed to simplify the calculation. The eigenfunctions, under this new definition, possess the orthogonality from which the expansion coefficients can be easily deduced. Selecting the optimum truncation of the series, we derive a closed system of simultaneous linear equations for the same number of the unknown reflection and transmission coefficients. The effects of several physical parameters, including the porosity, friction, width, and depth of the porous barrier, on the dispersion relation, reflection and transmission coefficients are discussed in detail through the graphical representations of the solutions. It is concluded that these parameters have certain impacts on the reflection and transmission energy.
