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A novel enhanced finite element method (EFEM) for the vibration analysis of two-dimensional linear elastics is presented in this work. The interpolation cover functions in the enhanced elements are the linear Lagrange polynomial basis function and a set of harmonic trigonometric functions. The harmonic trigonometric function originates from the spectral method, so the proposed method can be regarded as a combination of the classical finite element method and the spectral technique. The interpolation cover functions can be directly applied to the finite element model using low-order elements without any mesh adjustment. Meanwhile, the linear dependence problem in theEFEM is investigated in this work, and a simple and effective scheme is proposed to eliminate the linear dependence problem and ensure that the coefficient matrix in the EFEM is sparsely symmetric positive definite. Because the standard finite element approximation space is enhanced by the interpolation cover functions, the proposed EFEM in this work can obtain precision numerical solutions for two-dimensional linear elastic solid vibration analysis by even using a rough mesh, thus reducing the cost in mesh generation. Several typical numerical examples show that, compared with quadratic finite elements, the EFEM proposed in this work can not only provide more accurate numerical results, but also have higher computational efficiency.