On the Stability of Approximation Operators in Problems of Structural Dynamics
نویسنده
چکیده
Three direct integration schemes for the matrix equations of motion of structural dynamics-the Newmark generalized acceleration operator, the Wilson averaging variant of the linear acceleration operator and an averaging method based on a variational principle derived by Gurtin-are investigated for stability and approximation viscosity. Using established techniques developed by J. von Neumann and Lax and Richtmyer, the latter two approximation operators are found to be unconditionally stable. In addition, the constant average acceleration version of the Newmark method is found to be unconditionally stable and to possess no attenuation due to approximation viscosity. Truncation error due to the low-pass filtering characteristics of spatially discretized systems is highly damped by the Wilson averaging and Gurtin averaging operators; all three operators exhibit error in the period of the response which is a function of time step size.
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