상태방정식에 기반한 불균일한 1차원 구조물에 대한 주파수영역 스펙트럴요소모델

초록

In this study, the formulation procedure of frequency-domain spectral element model (SEM) for the non-uniform one-dimensional structure whose cross-sections or material properties vary in the length-wise direction is presented. The homogeneous governing equations of non-uniform one-dimensional structures are firstly transformed into the state-vector equations. By applying the differential transformation method (DTM) into the system matrices and state-vectors represented by the power series, extremely simple recurrence formulas for the coefficients of power series are obtained comparing to the prior researches in the literature. Using the computed coefficients of power series obtained from the recurrence formulas, the transfer matrices that relates the state-vectors at the left-end position and at the right-end position of a finite element are readily formulated. Finally, the spectral element matrices (i.e, the dynamic stiffness matrices) for the non-uniform one-dimensional structure are obtained from the transfer matrices. Using the numerical studies, the accuracy of the present SEM is verified by comparison with the well-known finite element method (FEM).