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Title: Accuracy of response of single-degree-of-freedom systems to ground motion
Authors: United States. Defense Nuclear Facilities Safety Board.
University of Tennessee at Martin.
Earthquake Engineering Research Program (U.S.)
Ebeling, Robert M., 1954-
Green, Russell A.
French, Samuel E., 1930-
Keywords: Earthquake engineering
Numerical methods
Mathematical methods
Time domain dynamic analysis
Hydraulic structures
Structural dynamics
Structural analysis
Publisher: Information Technology Laboratory (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Technical report (U.S. Army Engineer Waterways Experiment Station) ; ITL-97-7.
Description: Technical Report
Abstract: 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 function 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 β method (with values of γ and β that correspond to the linear acceleration method), the Wilson θ Method, the Central Difference Method, the 4th-order Runge-Kutta method, Duhamel's integral solved in a piecewise exact fashion, and the piecewise exact method applied directly. Much of the current guidance for selecting the time-step used in computing dynamic response to ground acceleration is based on studies of the accuracy of numerical methods for computing free vibration response of undamped SDOF systems. The information from the free vibration studies is often combined with useful, but qualitative, reference to the frequency characteristics of the forcing function. The time-step criteria for a specified level of accuracy are often expressed as a fraction of the natural (undamped) period of the SDOF system. This report quantifies how the accuracy of the six numerical step-by-step procedures is affected by the time-step and the ground motion frequency characteristics.
Rights: Approved for public release; distribution is unlimited.
Appears in Collections:Technical Report

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