Stability and Accuracy of Wilson－θ Method with Modified Acceleration

Abstract

There remain two kinds of the Wilson-θ methods, the Wilson-θ and methods named by author. In the Wilson-θ method, the accelerations are not modified by the dynamic equilibrium equations at the time ; in the Wilson-θ method, the accelerations are modified. The amplification matrixes of the Wilson-θ and methods for single-degree-of-freedom system are derived. The stabilities of the Wilson-θ and methods are examined by the spectral radii of the amplification matrixes. The stability of the Wilson-θ method is unconditional for . The calculation results indicate: the stability of the Wilson-θ method is not unconditional, its improvement of accuracy is slight; both the stability range and accuracy are less than the ones of the linear acceleration method, so the Wilson-θ method wouldn't be adopted.