Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,ar...Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.展开更多
The end effect on the output voltage of a twin-wire depth probe was investigated both theoretically and ex- perimentally.It was found that the contribution of the end of the probe to the output voltage depends upon th...The end effect on the output voltage of a twin-wire depth probe was investigated both theoretically and ex- perimentally.It was found that the contribution of the end of the probe to the output voltage depends upon the distance between the boundary and the end of the probe and the geometrical configuration of the probe. By mounting a piece of plate to the end of the electrodes,the end effect can be reduced.However,the size of the plate required to eliminate completely this effect is much larger than that usually mounted on commercially available probes.Comparison between theoretical and experimental results was made.Reasonable agreement was obtained.展开更多
基金NASI (National Academy of Sciences, India) for providing financial support
文摘Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.
文摘The end effect on the output voltage of a twin-wire depth probe was investigated both theoretically and ex- perimentally.It was found that the contribution of the end of the probe to the output voltage depends upon the distance between the boundary and the end of the probe and the geometrical configuration of the probe. By mounting a piece of plate to the end of the electrodes,the end effect can be reduced.However,the size of the plate required to eliminate completely this effect is much larger than that usually mounted on commercially available probes.Comparison between theoretical and experimental results was made.Reasonable agreement was obtained.
