Capability To Capture Dynamic Loading in Linear Dynamic Analysis of Single Degree of Freedom Systems
|Published in:||International Journal of Structural Stability and Dynamics, May 2013, n. 5, v. 13|
In this work, the importance of the capability to capture dynamic loading for an integration method is emphasized. In a step-by-step integration procedure, amplitude distortions in the transient and steady-state responses depend on the step discretization error of dynamic loading for each time step. Correlations between amplitude distortion and step discretization error for dynamic loadings are analytically established for a specified integration method. These correlations may be considered as the basic numerical properties in evaluating a step-by-step integration method. As a result, the superiority of the previously published algorithm (PPA) [S. Y. Chang, Int. J. Numer. Meth. Eng.77(8) (2009) 1100–1120] over its modified form and the member of Newmark family method (MNM) with β = γ = 1/2 in capturing dynamic loading is analytically verified (even though the three algorithms have exactly the same characteristic equation).
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