Scattering Of Flexural Wave In A Infinite Thin Plate With Multi-abribitray Cutouts

Thin plate structures are widely used in various types of engineering structures. To satisfy the engineering designs, it is inevitable to design the plate structure containing cutouts, which can cause stress concentrations. Stress concentrations greatly decrease the loading capacity of structures, and reduce the service life of structures. At present, the static stress concentrations of structures have been researched in detail. But the investigation of dynamic stress concentrations is not enough. Based on the Kirchhoff plate assumptions and employed the method of multi-coordinates method, rotated coordinates system, complex variable method and conformal mapping method, the scattering of the flexural wave was investigated by multi-arbitrary cutouts in an infinite plate. Multi-polar coordinates and rotated coordinates methods are meant to construct series form solution of scattering waves in global coordinates. Under each local coordinate the series satisfy the boundary conditions of arbitrary cutouts by method of conformal mapping. This can transform the scattering wave problem into the problem to solve the unknown coefficients of solution series. Thus the problem was converted into the problem of linear algebraic equations by method of truncation coefficient. The dynamic moment concentration factor was obtained by solving the scattering wave solution series coefficients. Some numerical examples were calculated in detail. The effect factor of dynamic moment concentration factor was discussed in different parameters.The paper's contributions focus on as follow: 1. Described a simplified infinite plate significance and frequency domain analysis significance in the application of practical engineering, the complex expression of equation internal force of plate is obtained by matrix method. 2. the scattering wave of the series expression in the global coordinate system were investigated by the method of multi-polar coordinate and series expression of scattering waves were given under each rotating local coordinate by the method of conformal mapping. The coefficients of the truncated scattering wave series expression were solved by boundary conditions of the hole in the mapping plane.3. the expression of dynamic moment concentration factor around the hole was derived. and dynamic moment concentration factor of horizontal double elliptical holes and triple elliptical holes varied with distance between the holes, incident angle and the dimensionless wave number.