共查询到20条相似文献，搜索用时 31 毫秒
1.
The construction of stationary expressions for quantities of physical interest such as radiated power and target strength is discussed broadly for acoustic problems involving radiation or scattering from finite objects of arbitrary shape. The Kirchhoff-Helmholtz integral corollaries of the wave equation, which express acoustic pressure at either interior or exterior points in terms of pressure and its normal derivative over any closed surface, yield for both interior and exterior problems two mathematically dissimilar but related functional relations between surface field quantities. One of these is the better known surface Helmholtz integral equation; the other is a differential-integral relation which involves the tangential derivatives of pressure on the surface. The four linear operators involved in these functional relations are studied and it is found that two are self-adjoint, while the other two are an adjoint pair. A general technique for constructing variational expressions recently developed by Gerjuoy et al. [28] is adapted to acoustic radiation and scattering problems with the functional relations taken as the primary governing relations. Included examples are stationary expressions for the radiated power when either the normal velocity or the pressure are specified on the surface (the other quantity being unknown) and the target strength for scattering from a rigid object. The adjoint relations allow simple physical interpretations for the Lagrange multipliers that arise in the theory, such that the guesses for good trial functions can take advantage of existing physical insight. It is demonstrated with a specific example (transversely vibrating disk) that the resulting estimate for radiated power is substantially more accurate than that of the trial function for surface pressure which was inserted into the stationary expression. 相似文献
2.
This paper deals with the solution of the title problem in the case where the outer boundary is subjected to uniform, hydrostatic pressure while the inner edge of the plate is free. It is assumed that the plate thickness varies (a) in a discontinuous fashion and (b) linearly.An approximate approach is proposed using polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge, only. The eigenvalues are determined using the optimized Rayleigh-Ritz method and good engineering agreement is shown to exist with buckling parameters obtained by means of a finite element code. 相似文献
3.
《Applied Ocean Research》2005,27(4-5):224-234
The modified scaled boundary finite-element method (SBFEM), keeping the advantages of the original SBFEM, eliminates the restriction of the scaling center location so that this approach can solve two-dimensional problems with parallel side-faces. In this paper, the modified SBFEM is applied to solutions of two types of problems—wave diffraction by a single and twin surface rectangular obstacles and wave radiation induced by an oscillating mono-hull and twin-hull structures in a finite depth of water. For wave diffraction problems, numerical results agree extremely well with the analytic solution for the single obstacle case and other numerical results of a different approach for the twin obstacle case. For wave radiation problems, the particular solutions to the scaled boundary finite-element equation are presented for cases of heave, sway and roll motions. The added mass and damping coefficients for heave, sway and roll motions of a two-dimensional rectangular container are computed and the numerical results are compared with those from independent analytical solution and numerical solution using the boundary element method (BEM). It is found that the SBFEM method achieves equivalent accuracy to the conventional BEM with only a few degrees of freedom. In the last example, wave radiation by a two-dimensional twin-hull structure is analyzed. Comparisons of the results with those obtained using conventional Green's function method (GFM) demonstrate that the method presented in this paper is free from the irregular frequency problems. 相似文献
4.
This study gives a new approximate analytic solution for water wave scattering by a submerged horizontal porous disk in the context of the linear potential theory. The solution is based on the domain decomposition method. The velocity potentials are determined by two different approaches. One approach is to adopt decompositions for velocity potentials, and the other is to expand the vertical derivative of the velocity potential on the porous disk along the radial direction. Hence the velocity potentials are determined by the matched eigenfunction expansions. Differing from previous solutions with respect to the porous disk, the present solution needs no complex dispersion relations. Thus the new solution is easier for numerical implementation. According to numerical examples, the convergence of the present solution is satisfactory. In addition, the present predictions of the wave surface elevation and the vertical wave force on the disk agree very well with previous results by different approaches. The present solution can also be extended to other structures involving disks, such as a fish cage, a porous disk with finite thickness, and a submerged elastic disk. 相似文献
5.
《Ocean Modelling》2003,5(1):37-63
A stabilized finite-element (FE) algorithm for the solution of oceanic large scale circulation equations and optimization of the solutions is presented. Pseudo-residual-free bubble function (RFBF) stabilization technique is utilized to enforce robustness of the numerics and override limitations imposed by the Babuška–Brezzi condition on the choice of functional spaces. The numerical scheme is formulated on an unstructured tetrahedral 3d grid in velocity–pressure variables defined as piecewise linear continuous functions. The model is equipped with a standard variational data assimilation scheme, capable to perform optimization of the solutions with respect to open lateral boundary conditions and external forcing imposed at the ocean surface. We demonstrate the model performance in applications to idealized and realistic basin-scale flows. Using the adjoint method, the code is tested against a synthetic climatological data set for the South Atlantic ocean which includes hydrology, fluxes at the ocean surface and satellite altimetry. The optimized solution proves to be consistent with all these data sets, fitting them within the error bars.The presented diagnostic tool retains the advantages of existing FE ocean circulation models and in addition (1) improves resolution of the bottom boundary layer due to employment of the 3d tetrahedral elements; (2) enforces numerical robustness through utilization of the RFBF stabilization, and (3) provides an opportunity to optimize the solutions by means of 3d variational data assimilation. Numerical efficiency of the code makes this a desirable tool for dynamically constrained analyses of large datasets. 相似文献
6.
The radiation and diffraction problems are considered in the frequency domain for a thin elastic plate of rectangular planform floating in an irrotational, incompressible ocean of infinite depth. The inner potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion which suits the geometry and zero-draft nature of the plate. Problems associated with distributing sources in the free surface are avoided. The Chen and Mei variational principle is used to weakly match this inner solution and its normal derivative to an outer field described by distributing sources on the exterior of the hemisphere. The validity of the procedure is first illustrated by considering a heaving circular disk. Numerous hydrodynamic coefficients are presented as benchmark data for floating flexible structures. The transient motion of the plate is simulated using rational approximations (in the frequency domain) to the radiation impedance and diffraction mapping which are implemented as ODE's in the time domain. 相似文献
7.
Hydroelastic analysis of fully nonlinear water waves with the floating elastic plate is a hard mission. Especially, the behavior of the wave would be more complex when water wave encounter the floating elastic plate. In this paper, the meshless numerical method is devoted to solve such a problem. Fundamental solution method is applied to approximate the velocity potential in the fluid domain. When the water wave encounters the plate, the wave function would not be enough smooth in the edge of plate compared to the other points. Hence, to analyze numerically the behavior of wave, the solution space should include the basis functions that are not enough smooth in the edge of plate. Moreover, to decrease computational cost significantly, the basis functions had better to have local compact support. The multiple knot B-spline basis functions are suitable that contain both properties. The number of repeated knots, the degree of B-spline and the spatial points are challengeable that are discussed in this paper. The results are in good agreement with those obtained from other numerical works. 相似文献
8.
9.
A higher order panel method based on B-spline representation for both the geometry and the solution is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then shown to be evaluated using conventional numerical quadrature. By selecting a proper order for numerical quadrature, the accuracy of the present method can be increased to the machine limit. The far- and near-field influences are shown to be evaluated based on the same far-field approximation, but the near-field solution requires subdividing the panels into smaller subpanels continuously, which can be effectively implemented due to the B-spline representation of the geometry. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution on the blade surface, including very close to the tip and trailing edge regions, with far fewer panels than existing low-order panel methods. 相似文献
10.
G. X. WuR. Eatock Taylor 《Applied Ocean Research》1994,16(6):363-372
The two-dimensional nonlinear time domain free surface flow problem is analyzed by the finite element method. Two approaches are used. One is based on the velocity potential which is approximated by means of shape functions. The solution is obtained through use of a variational statement, and the velocity is obtained subsequently by the Galerkin method. The other approach is to write both potential and velocity in terms of the shape functions at the same time. Their solutions are derived from the same equation by using another variational statement. Numerical results are given for the vertical wave maker problem and for a transient wave in a rectangular container. They are compared with analytical solutions, and very good agreement is found. 相似文献
11.
A high-order Rankine panel method based on Non-Uniform Rational B-Spline (NURBS) is developed for solving the three-dimensional radiation and diffraction problems with forward speed. A NURBS surface is used to precisely represent the body geometry. Velocity potential on the body surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to numerical computation and the integral equations are evaluated by applying Gauss–Legendre quadrature. The mj-terms are evaluated by a desingularized method which utilizes NURBS technique. In order to verify the method proposed, it is firstly applied to the unbounded flow problem of a sphere and spheroids. The numerical results are found to be in good agreement with analytical solutions. Then the method is used to solve the radiation and diffraction problems of a sphere and the diffraction problem of a spheroid moving with a forward speed beneath the free surface in frequency domain. The numerical results are satisfactory in comparison with the published analytical results and experimental results. 相似文献
12.
Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples. 相似文献
13.
We propose a new method for the evaluation of the velocities of surface currents according to the data of measurements carried
out by using high-frequency land-based radars. The method is based on the representation of the velocity fields via two scalar
potentials, expansion of these potentials in series in basis functions, and determination of the coefficients of expansion
according to the data of radar measurements as solutions of the corresponding variational problems. The errors of the procedure
of determination of the coefficients of expansion are removed by using a special regularization procedure based on information
theory. The proposed method enables one to fill gaps in the space and time series of radar measurements. We illustrate the
method by an example of numerical analysis of mesoscale and submesoscale (10–50 km) surface currents in the Monterey Bay (California,
USA) performed on the basis of the data of radar measurements carried out in August 1994.
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Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 24–36, March–April, 2005. 相似文献
14.
《Ocean Engineering》2004,31(3-4):269-304
The paper seeks to apply the methodology of matched asymptotic expansions to obtain analytical solutions for hydrodynamic properties of a circular cylindrical platform (truncated circular cylinder) in extremely shallow water. By matching potentials of the fluid flows outside and under the cylinder bottom with the inner flow near its edge the radiation problems are solved for heave, surge and pitch motions. Closed asymptotic formulae are derived for all hydrodynamic coefficients of the floating cylinder, which include the first-order terms in the gap height. The formulae are discussed and shown to compare well with numerical results published in literature. 相似文献
15.
The present paper, of a tutorial nature, solves two different thermoelastic problems using a unified approach: (a) thermoelastic stresses and deflections in thin, rectangular plates with edges elastically restrained against rotation when small-deflection theory is used and stress resultants in the middle plane of the plates are neglected; and (b) thermoelastic plane stress situations in rectangular plates with stress-free edges subjected to a two-dimensional temperature distribution.The first problem is attacked using polynomial coordinate functions which identically satisfy the governing boundary conditions, and the Ritz method is used to determine the plate response. When the flexibility coefficients approach zero (clamped edge conditions) the calculated results practically coincide with the exact solution for the test case treated in this paper. On the other hand this degenerate solution turns out to be a very convenient approximation for obtaining a solution to Airy's problem described in the second place and which is also solved in a straightforward manner using a variational approach. 相似文献
16.
Wave-induced transient response of seabeds is numerically analyzed through a radial point interpolation meshless method (radial PIM). The Biot’s consolidation theory is employed and incorporated with virtual boundary conditions to describe this wave-induced transient response of the seabed. Displacement and pore water pressure are spatially discretized by the radial PIM with the same shape function. Compactly supported basis functions are proposed to obtain a banded system equation. Because the radial PIM passes through all nodal points within an influence domain, essential boundary conditions as well as virtual boundary conditions can be easily implemented at local level. Fully implicit integration scheme is used in time domain to avoid spurious ripple effect. The proposed algorithm is assessed through the comparison of numerical results with closed-form solution or finite element solutions. 相似文献
17.
The asymmetric three-dimensional radiation pattern and resultant elastodynamic response of stress waves in a model comprising a compressible water column overlying a transversely isotropic seabed in which a time-harmonic source acts is theoretically investigated. The use of potential functions, the Hankel transform, and a Fourier series expansion are adopted to deal with the equations of motion for both media. Closed-form integral expressions are developed for the potentials and the stress/displacement components. The expressions and introduced procedure are sufficiently flexible to incorporate various types of source loads. To evaluate the field quantities, the residue method and a robust integration scheme are utilized to handle the poles and branch points within the integrand. Any possible number of dispersive propagation modes are taken into account in the integral evaluation. The deduced velocity dispersion curves depict the characteristics of the various modes. They also indicate the existing singular points (poles) for a specific dimensionless frequency and the surface wave type associated with each pole. Numerical results are presented for the hydrodynamic pressure and displacement in the liquid layer and stress and displacement components in the solid seabed due to distributed and concentrated source excitations. The formulation and the numerical scheme are valid for calculating the wavefield anywhere within the model including both far- and near-field effects. The sensitivity of the results to different parameters is also analyzed. Both analytical and numerical comparisons with existing solutions for simpler cases are made to confirm the validity of the results. The results are especially useful in seismic hazard assessment of submarine earthquakes, landslides, and tsunamis. They can also be extended to deal with the fluid-solid-structure interaction problems. 相似文献
18.
The hydrodynamic problem of a hydrofoil travelling at constant speed in water waves has been investigated through velocity potential theory. The boundary conditions on the free surface have been linearized, and the effects are accounted for through the Green function. The overall problem is decomposed into the steady forward speed problem and periodic wave radiation and diffraction problems. Each of these problems is solved using the boundary integral equation over the hydrofoil surface together with a vortex sheet behind the trailing edge. The body surface boundary condition is imposed on its mean position. As a result the steady potential will contribute a well-known mj term to the body surface boundary condition on the radiation problem. The numerical difficulty in dealing with this term is effectively resolved through a difference method. The effects of the thickness on the wave radiation and diffraction are investigated. The applicability of various reciprocity relationships in this problem is discussed. 相似文献
19.
20.
Shen Wang 《Ocean Engineering》1981,8(6):599-621
The radiation problem for two parallel-spaced cylinders is studied. The solution is expressed explicitly in terms of well-behaved convergent series with elementary functions, which are convenient for numerical computation and readily applicable for two-dimensional two-body potential problems. The added mass and damping coefficients together with the phase angles of radiated wave potentials for the forced heave and sway motions of two identical submerged cylinders are presented. The results are useful for determination of the hydrodynamic properties of multi-hull semi-submersibles. In view of the close relationship between a radiation and a scattering problem, the application of the results to the problem of energy extraction from water waves is also noted. 相似文献