improvement of numerical manifold method using nine-node ‎quadrilateral and ten-node triangular elements along with ‎complex fourier rbfs in modeling free and forced vibrations

In this paper, the numerical manifold method (nmm) with a 9node quadrilateral element and a 10node triangular element is developed. furthermore, complex fourier shape functions are used to improve the 9node quadrilateral nmm. also, the two approaches of higherorder nmm construction are compared, increasing the order of weight functions or local approximation ones; for this purpose, sixnode triangular and threenode triangular using secondorder and thirdorder nmm is used. for validation of the suggested method, one free vibration and two forced vibration numerical examples are assessed. the results show that the proposed methods are more accurate than conventional nmm. in addition, the superiority of complex fourier shape functions compared to classical lagrange ones in improving accuracy is perceived.