Accuracy of Response of Single-Degree-of-Freedom Systems to Ground Motion
ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG MS INFORMATION TECHNOLOGY LAB
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This technical report summarizes an assessment of the accuracy of six numerical step by step procedures used in computational structural dynamics. The results provide quantitative guidance on how the accuracy of these procedures is affected by the time step and the ground motion frequency characteristics. The six procedures evaluated in this study are representative of the different types of numerical algorithms used to compute the dynamic structural response to a time dependent loading. The time dependent loading is expressed in terms of a ground acceleration time history. The dynamic structural response for each structural model is characterized by the computed response time histories of accelerations, velocities, and displacements. Using single-degree-of-freedom SDOF models with natural periods assigned based on consideration of the important modal periods of hydraulic structures, an evaluation is made of the accuracy of the computed responses at regular time increments during ground shaking. A ground acceleration applied at the base of an SDOF system is equivalent to a fixed base SDOF system with the forcing fimction applied to the mass. The results show a correlation between the accuracy of the six numerical step-by-step procedures with the time step value and frequency characteristics of the ground motion used in the analyses. The six algorithms included in this study are the Newmark beta method with values of gamma and beta that correspond to the linear acceleration method, the Wilson theta Method, the Central Difference Method, the 4th order Runge-Kutta method, Duhamels integral solved in a piecewise exact fashion, and the piecewise exact method applied directly.