지역 극좌표계를 이용한 임의 형상 자유단 평판의 자유진동해석을 위한 무요소법 개발

A new meshless method for obtaining natural frequencies of arbitrarily shaped plates with the free boundary condition is introduced in the paper. In order to improve the characteristics of convergence and accuracy of the method, a special local polar coordinates system is devised and located for each of nodes distributed along the boundary of the plate of interest. In addition, a new way of decreasing the size of the system matrix that gives natural frequencies of the plate is employed to reduce the amount of numerical calculations, which is needed for computing the determinant of the system matrix. Finally, the excellence of the characteristics of convergence and accuracy of the method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate and converged swiftly to exact values as the number of boundary nodes increases.