Free Vibration Analysis of Arbitrarily Shaped Plates with Free Edges Using Non-dimensional Dynamic Influence Functions: the case that straight and curved boundaries are mixed

무차원 동영향 함수를 이용한 자유단 경계를 가진 임의 형상 평판의 진동해석 : 직선 및 곡선 경계가 혼합된 경우

Free Vibration Analysis using Non-dimensional Dynamic Influence Function (NDIF) is extended to arbitrarily shaped plates including polygonal plates. Since the corners of polygonal plates have indefinite normal directions and additional boundary conditions related to a twisting moment at a corner along with moment and shear force zero conditions, it is not easy to apply the NDIF method to polygonal plates wi th the free boundary condition. Moreover, owing to the fact that the local polar coordinate system, which has been introduced for free plates with smoothly varying edges, cannot be employed for the straight edges of the polygonal plates, a new coordinate system is required for the polygonal plates. These problems are solved by developing the new method of modifying a corner into a circular arc and setting the normal direction at the corner to an average value of normal direct ions of two edges adjacent to the corner. Some case studies for plates with various shapes show that the proposed method gives credible natural frequencies and mode shapes for various polygons that agree well with those by an exact method or FEM (ANSYS).