The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia...The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.展开更多
This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe...This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.展开更多
This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
The hydroelastic interaction of an incident wave with a semi-infinite horizontal elastic plate floating on a homogenous fluid of finite depth is analyzed using the eigenfunction expansion method. The fluid is assumed ...The hydroelastic interaction of an incident wave with a semi-infinite horizontal elastic plate floating on a homogenous fluid of finite depth is analyzed using the eigenfunction expansion method. The fluid is assumed to be inviscid and incompressible and the wave amplitudes are assumed to be small. A two-dimensional problem is formulated within the framework of linear potential theory. The fluid domain is divided into two regions, namely an open water region and a plate-covered region. In this paper, the orthogonality property of eigenfunctions in the open water region is used to obtain the set of simultaneous equations for the expansion coefficients of the velocity potentials and the edge conditions are included as a part of the equation system. The results indicate that the thickness and the density of plate have almost no influence on the reflection and transmission coefficients. Numerical analysis shows that the method proposed here is effective and has higher convergence than the previous results.展开更多
For a generalized radiation problem,an infinitely long submerged horizontal cylinder is forced to vibrate periodically in the transverse direction,with a described elastic harmonic motion along its longitudinal direct...For a generalized radiation problem,an infinitely long submerged horizontal cylinder is forced to vibrate periodically in the transverse direction,with a described elastic harmonic motion along its longitudinal direction.A critical frequency corresponds to the described wave number of elastic vibration,and the generalized hydrodynamic coefficients abruptly change in the vicinity of critical frequency.In this work,a numerical examination is carried out to study the characteristics of wave profiles and wave propagation in the vicinity of the critical frequency.Results show that below the critical frequency,the real parts of complex wave profiles have large values in the vicinity of the cylinder and decay to zero with the increasing distance from the cylinder.Meanwhile,the imaginary parts of complex wave profiles are all zero,which explains why the generalized radiation damping is zero when the vibration is less than the critical frequency.At far distances,no radiation wave is observed.When the vibration exceeds the critical frequency,the real and imaginary parts of the wave profiles oscillate harmonically and keep steady amplitudes.In addition,the generated radiation wave propagates obliquely outward.The influence of the cylinder’s submergence depth on the wave profile is also studied,and the results indicate that the amplitude of the wave profile decreases as the submergence depth of the cylinder increases.The 3D wave profiles are graphically presented to show the wave propagation characteristics in the vicinity of the critical frequency for this generalized radiation problem.This study provides a good reference for the interaction between fluid and slender elastic structures.展开更多
Boundary Collocation Method （BCM） based on Eigenfunction Expansion Method （EEM）, a new numerical method for solving two-dimensional wave problems, is developed. To verify the method, wave problems on a series of b...Boundary Collocation Method （BCM） based on Eigenfunction Expansion Method （EEM）, a new numerical method for solving two-dimensional wave problems, is developed. To verify the method, wave problems on a series of beaches with different geometries are solved, and the errors of the method are analyzed. The calculation firmly confirms that the results will be more precise if we choose more rational points on the beach. The application of BCM, available for the problems with irregular domains and arbitrary boundary conditions, can effectively avoid complex calculation and programming. It can be widely used in ocean engineering.展开更多
The wave interaction with stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed based on the small amplitude wave theory.The study is performed to analyse the effect...The wave interaction with stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed based on the small amplitude wave theory.The study is performed to analyse the effectiveness of partial porous structure in increasing the wave attenuation in the nearshore regions consisting of stratified porous structures of different configurations using the eigenfunction expansion method and orthogonal mode-coupling relation.The hydrodynamic characteristics such as wave reflection coefficient,transmission coefficient,dissipation coefficient,wave force impact and surface elevation are investigated due to the presence of both horizontally and vertically stratified porous structures.The effect of varying porosity,structural width,angle of incidence,wavelength and length between the porous block and stratified structure is examined.The numerical results are validated with the results available in the literature.The present study illustrates that the presence of the stratified structure decreases wave transmission and efficient wave attenuation can also be easily achieved.The wave force acting on stratified structure can be decreased if the structure is combined with wider surface-piercing porous blocks.Further,the presence of stratified porous structure combined with porous block helps in creating a tranquil zone in the leeside of the structure.The combination of vertical and horizontal stratified porous structure with surface-piercing porous block is intended to be an effective solution for the protection of coastal facilities.展开更多
This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block ...This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.展开更多
To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to ...To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ（τ is nondimensional time） equals 0.1 near the boundaries of ζ =1 （ζ is nondimensional space coordinate） and ζ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate 4.展开更多
Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expans...Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expansion method is used to obtain the diffraction and radiation solutions when the converter width tends to be infinity. The trapezoidal section of the converter is approximated by a rectangular section for simplification. The nonlinear viscous damping effects are accounted for by including a drag term in the two- and three-dimensional methods. It is found that the three- dimensional results are in good agreement with the two-dimensional results when the converter width becomes larger, especially when the converter width is infinity, which shows that both of the methods are reasonable. Meantime, it is also found that the peak value of the conversion efficiency decreases as the converter width increases in short wave periods while increases when the converter width increases in long wave periods.展开更多
Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip was applied by tension “ p ' in y_ direction. The boundary value...Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip was applied by tension “ p ' in y_ direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T _stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.展开更多
It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal...It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.展开更多
A 2-D semi-analytical model of double gate （DG） tunneling field-effect transistor （TFET） is proposed. By aid of introducing two rectangular sources located in the gate dielectric layer and the channel, the 2-D Poi...A 2-D semi-analytical model of double gate （DG） tunneling field-effect transistor （TFET） is proposed. By aid of introducing two rectangular sources located in the gate dielectric layer and the channel, the 2-D Poisson equation is solved by using a semi-analytical method combined with an eigenfunction expansion method. The expression of the surface potential is obtained, which is a special function for the infinite series expressions. The influence of the mobile charges on the potential profile is taken into account in the proposed model. On the basis of the potential profile, the shortest tunneling length and the average electrical field can be derived, and the drain current is then constructed by using Kane＇s model. In particular, the changes of the tunneling parameters Ak and Bk influenced by the drain-source voltage are also incorporated in the predicted model. The proposed model shows a good agreement with TCAD simulation results under different drain-source voltages, silicon film thicknesses, gate dielectric layer thicknesses, and gate dielectric layer constants. Therefore, it is useful to optimize the DG TFET and this provides a physical insight for circuit level 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
基金Supported by the National Natural Science Foundation of China under Grant No.10962004the Natural Science Foundation of Inner Mongolia under Grant No.2009BS0101+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002the Cultivation of Innovative Talent of "211 Project"of Inner Mongolia University
文摘The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.
基金Project supported by the National Natural Science Foundation of China (No. 10962004)the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)
文摘This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
基金supported by the Innovation Program of Shanghai Municipal Education Commission (Grant No. 09YZ04)the State Key Laboratory of Ocean Engineering (Grant No. 0803)the Shanghai Rising-Star Program (Grant No. 07QA14022)
文摘The hydroelastic interaction of an incident wave with a semi-infinite horizontal elastic plate floating on a homogenous fluid of finite depth is analyzed using the eigenfunction expansion method. The fluid is assumed to be inviscid and incompressible and the wave amplitudes are assumed to be small. A two-dimensional problem is formulated within the framework of linear potential theory. The fluid domain is divided into two regions, namely an open water region and a plate-covered region. In this paper, the orthogonality property of eigenfunctions in the open water region is used to obtain the set of simultaneous equations for the expansion coefficients of the velocity potentials and the edge conditions are included as a part of the equation system. The results indicate that the thickness and the density of plate have almost no influence on the reflection and transmission coefficients. Numerical analysis shows that the method proposed here is effective and has higher convergence than the previous results.
基金supported by the National Key Research and Development Program of China(2022YFB2602800)National Natural Science Foundation of China(No.52271261).
文摘For a generalized radiation problem,an infinitely long submerged horizontal cylinder is forced to vibrate periodically in the transverse direction,with a described elastic harmonic motion along its longitudinal direction.A critical frequency corresponds to the described wave number of elastic vibration,and the generalized hydrodynamic coefficients abruptly change in the vicinity of critical frequency.In this work,a numerical examination is carried out to study the characteristics of wave profiles and wave propagation in the vicinity of the critical frequency.Results show that below the critical frequency,the real parts of complex wave profiles have large values in the vicinity of the cylinder and decay to zero with the increasing distance from the cylinder.Meanwhile,the imaginary parts of complex wave profiles are all zero,which explains why the generalized radiation damping is zero when the vibration is less than the critical frequency.At far distances,no radiation wave is observed.When the vibration exceeds the critical frequency,the real and imaginary parts of the wave profiles oscillate harmonically and keep steady amplitudes.In addition,the generated radiation wave propagates obliquely outward.The influence of the cylinder’s submergence depth on the wave profile is also studied,and the results indicate that the amplitude of the wave profile decreases as the submergence depth of the cylinder increases.The 3D wave profiles are graphically presented to show the wave propagation characteristics in the vicinity of the critical frequency for this generalized radiation problem.This study provides a good reference for the interaction between fluid and slender elastic structures.
基金financially supported by the Special Fund for Marine Renewable Energy Projects(Grant Nos.GHME2010GC01 and GHME2013ZB01)the National Natural Science Foundation of China(Grant Nos.51109201 and 41106031)
文摘Boundary Collocation Method （BCM） based on Eigenfunction Expansion Method （EEM）, a new numerical method for solving two-dimensional wave problems, is developed. To verify the method, wave problems on a series of beaches with different geometries are solved, and the errors of the method are analyzed. The calculation firmly confirms that the results will be more precise if we choose more rational points on the beach. The application of BCM, available for the problems with irregular domains and arbitrary boundary conditions, can effectively avoid complex calculation and programming. It can be widely used in ocean engineering.
基金Science and Engineering Research Board(SERB),Department of Science&Technology(DST),Government of India for supporting financially under the research grant No.CRG/2018/004184Ministry of Ports,Shipping and Waterways,Government of India through the research grant No.DW/01013(13)/2/2021.
文摘The wave interaction with stratified porous structure combined with a surface-piercing porous block in a stepped seabed is analysed based on the small amplitude wave theory.The study is performed to analyse the effectiveness of partial porous structure in increasing the wave attenuation in the nearshore regions consisting of stratified porous structures of different configurations using the eigenfunction expansion method and orthogonal mode-coupling relation.The hydrodynamic characteristics such as wave reflection coefficient,transmission coefficient,dissipation coefficient,wave force impact and surface elevation are investigated due to the presence of both horizontally and vertically stratified porous structures.The effect of varying porosity,structural width,angle of incidence,wavelength and length between the porous block and stratified structure is examined.The numerical results are validated with the results available in the literature.The present study illustrates that the presence of the stratified structure decreases wave transmission and efficient wave attenuation can also be easily achieved.The wave force acting on stratified structure can be decreased if the structure is combined with wider surface-piercing porous blocks.Further,the presence of stratified porous structure combined with porous block helps in creating a tranquil zone in the leeside of the structure.The combination of vertical and horizontal stratified porous structure with surface-piercing porous block is intended to be an effective solution for the protection of coastal facilities.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10962004 and 11061019)the Doctoral Foundation of Inner Mongolia(Grant Nos.2009BS0101 and 2010MS0110)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)the Chunhui Program of the Ministry of Education of China(Grant No.Z2009-1-01010)
文摘This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.
基金Projects(50576007,50876016) supported by the National Natural Science Foundation of ChinaProjects(20062180) supported by the National Natural Science Foundation of Liaoning Province,China
文摘To make heat conduction equation embody the essence of physical phenomenon under study, dimensionless factors were introduced and the transient heat conduction equation and its boundary conditions were transformed to dimensionless forms. Then, a theoretical solution model of transient heat conduction problem in one-dimensional double-layer composite medium was built utilizing the natural eigenfunction expansion method. In order to verify the validity of the model, the results of the above theoretical solution were compared with those of finite element method. The results by the two methods are in a good agreement. The maximum errors by the two methods appear when τ（τ is nondimensional time） equals 0.1 near the boundaries of ζ =1 （ζ is nondimensional space coordinate） and ζ =4. As τ increases, the error decreases gradually, and when τ =5 the results of both solutions have almost no change with the variation of coordinate 4.
基金supported by the Special Fund for Marine Renewable Energy of the Ministry of Finance of China(No.GD2010ZC02)
文摘Based on two- and three-dimensional potential flow theories, the width effects on the hydrodynamics of a bottom-hinged trapezoidal pendulum wave energy converter are discussed. The two-dimensional eigenfunction expansion method is used to obtain the diffraction and radiation solutions when the converter width tends to be infinity. The trapezoidal section of the converter is approximated by a rectangular section for simplification. The nonlinear viscous damping effects are accounted for by including a drag term in the two- and three-dimensional methods. It is found that the three- dimensional results are in good agreement with the two-dimensional results when the converter width becomes larger, especially when the converter width is infinity, which shows that both of the methods are reasonable. Meantime, it is also found that the peak value of the conversion efficiency decreases as the converter width increases in short wave periods while increases when the converter width increases in long wave periods.
文摘Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip was applied by tension “ p ' in y_ direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM ( eigenfunction expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T _stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.
文摘It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.
基金Project supported by the National Natural Science Foundation of China(No.61376106)the Graduate Innovation Fund of Anhui University
文摘A 2-D semi-analytical model of double gate （DG） tunneling field-effect transistor （TFET） is proposed. By aid of introducing two rectangular sources located in the gate dielectric layer and the channel, the 2-D Poisson equation is solved by using a semi-analytical method combined with an eigenfunction expansion method. The expression of the surface potential is obtained, which is a special function for the infinite series expressions. The influence of the mobile charges on the potential profile is taken into account in the proposed model. On the basis of the potential profile, the shortest tunneling length and the average electrical field can be derived, and the drain current is then constructed by using Kane＇s model. In particular, the changes of the tunneling parameters Ak and Bk influenced by the drain-source voltage are also incorporated in the predicted model. The proposed model shows a good agreement with TCAD simulation results under different drain-source voltages, silicon film thicknesses, gate dielectric layer thicknesses, and gate dielectric layer constants. Therefore, it is useful to optimize the DG TFET and this provides a physical insight for circuit level 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.
