Dissipation of Higher Mode using Numerical Integration Algorithm in Dynamic Analysis

In general dynamic analyses, lower mode response is of interest, however the higher modes of spatially discretized equations generally do not represent the real behavior and not affects to global response much. Some implicit algorithms, therefore, are introduced to filter out the high-frequency modes using intended numerical error. The objective of this study is to introduce the P-method and PC α-method to compare that with dissipation method and Newmark method through the stability analysis and numerical example. PC α-method gives more accuracy than other methods because it based on the α-method inherits the superior properties of the implicit α-method. In finite element analysis, the PC α-method is more useful than other methods because it is the explicit scheme and it achieves the second order accuracy and numerical damping simultaneously.

Authors:

• Jin Sup Kim
• Woo Young Jung
• Minho Kwon

Keywords:

• Dynamic
• α-Method
• P-Method
• PC α-Method
• Newmark method.

References:

[1] Bathe K. J. and Wilson E. L., Numerical Methods in Finite Element
Analysis. Printice-Hall, 1976.
[2] Hilber, H. M., Hughes T. J. R. and Taylor, R. L, "Improved Numerical
dissipation for time integration algorithms in Structural Dynamics."
Earthquake Engineering and Structural Dynamics, vol.5, No.3,
pp.283-292. 1977.
[3] Miranda, I., Ferencz R. M. and Hughes, T. J. R. "An Improved
Implicit-Explicit time Integration method for Structural Dynamics."
Earthquake Engineering and Structural Dynamics, Vol.18, No.5,
pp.643-653. 1989.
[4] Chang, S. Y, "Improved Numerical Dissipation for Explicit Methods in
Pseudo-dynamic Test."Earthquake Engineering and Structural
Dynamics, Vol.26, No.9, pp.917-930. 1997.