CAPABILITY TO CAPTURE DYNAMIC LOADING IN LINEAR DYNAMIC ANALYSIS OF SINGLE DEGREE OF FREEDOM SYSTEMS

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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Categorization of Dynamic Loading Into Force-Controlled Loading and Displacement-Controlled Loading

Volume 8: Seismic Engineering ◽

10.1115/pvp2018-85098 ◽

2018 ◽

Author(s):

Ichiro Tamura ◽

Shinichi Matsuura ◽

Ryuya Shimazu ◽

Koji Kimura

Keyword(s):

Dynamic Loading ◽

Kinematic Hardening ◽

Harmonic Excitation ◽

Degree Of Freedom ◽

Skeleton Curve ◽

Single Degree Of Freedom ◽

Single Degree ◽

Dynamic Loadings ◽

Restoring Forces

To investigate the behavior of inelastic single-degree-of-freedom systems, the maximum restoring forces and maximum deformations of the systems due to a harmonic excitation are calculated and drawn as a diagram. These systems have restoring forces characterized by bilinear skeleton curve of the kinematic hardening type. The diagram shows two types of characteristics, and the dynamic loadings can be categorized into force-controlled loading and displacement-controlled loading.

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Discretization of Dynamic Loading in Time History Analysis

Journal of Mechanics ◽

10.1017/jmech.2013.68 ◽

2013 ◽

Vol 30 (1) ◽

pp. 57-65

Author(s):

S.-Y. Chang

Keyword(s):

Dynamic Loading ◽

Amplification Factor ◽

Integration Method ◽

Time History ◽

Discretization Error ◽

Amplitude Error ◽

History Analysis ◽

Asymptotic Constant ◽

Error Amplification ◽

General Step

ABSTRACTAlthough the numerical properties of a step-by-step integration method can be evaluated based on the currently available techniques, there is still lack of a technique for evaluating its capability to capture dynamic loading. In this work, the amplitude error caused by the step discretization error is identified and the correlation between the relative amplitude error and relative step discretization error is analytically established. As a result, it is thoroughly confirmed that the asymptotic constant of the discretization error amplification factor for the displacement response to a cosine loading can be considered as an indicator of the capability to capture dynamic loading for a general step-by-step integration method.

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