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A n-sided polygonal cell-based smoothed finite element method (nCS-FEM) was recently proposed to analyze the elastic solid mechanics problems, in which the problem domain
can be discretized by a set of polygons with an arbitrary number of sides. In this paper, the nCS-FEM is further extended to the free and forced vibration analyses of two-dimensional (2D) dynamic problems. A simple lump mass matrix is proposed and hence the complicated integrations related to computing the consistent mass matrix can be
avoided in the nCS-FEM. Several numerical examples are investigated and the results found of the nCS-FEM agree well with exact solutions and with those of others FEM.
Keywords: Numerical methods; finite element method (FEM); cell-based smoothed finite element method (CS-FEM); polygonal element; n-sided polygonal cell-based smoothed finite element method (nCS-FEM).