Numerical Analysis Of Acoustic Scattering Of Underwater Objects Based On ? Finite Element Method

When using the classical finite element method, the well-known pollution error caused by the numerical dispersion will make it hard to get accurate results to the Helmholtz equation with large wave number This numerical dispersion error is rooted at the overly-stiff feature of the finite element model. Liu et al. have proposed smoothed finite element method by combining the strain smoothing technique and the classical finite element method. Node-based smoothed finite element method is one kind of the smoothed finite element method. However,NS-FEM always provides upper bound solution to the exact one in energy form for elasticity problems with homogeneous essential boundary conditions. Then Liu et al. proveide an alpha finite element method for acoustic problem by conbining the smaller wave number model of FEM and the large wave number model of NS-FEM through a scaling factor ?. The motivation for the this combined approach is essential from the feature of overly-stiff FEM model and overly-soft NS-FEM model. A technique is proposed to determine a particular alpha with which the ?-FEM model can possess a very close-to-exact stiffness, which can effectively reduce the dispersion error leading to dispersion free solutions for acoustic problems. This paper comculates the acoustic scatter field of some single objects and some double objects:(1) The ?-FEM governing equation for external acoustic problems is provided by combining the finite element method, the node-based smoothed finite element method and the Dt N boundary condition.(2) The external acoustic field of an infinite long rigid cylinder is calculated with ?-FEM and FEM. The ?-FEM solution and the FEM solution are compared to the exact solution to show the accuray of the ?-FEM.(3) The external acoustic of double infinite long rigid cylinders is calculated with the ?-FEM. The result show law of the souond pressure distribution and the intervene.(4) A double cylinders model is proposed and time domain analysis is done.