A numerical method for equation of motion in dynamic analysis of discrete structures

Authors

  • Nguyen Trong Phuoc
    Ho Chi Minh City University of Technology, VN
  • Do Kien Quoc

Keywords:

Numerical method; equation of motion; time step; acceleration; accuracy

Abstract

In this paper, a time step integration method for resolving the differential equation of motion of discrete structures subjected to dynamic loads is presented. This method is derived based on the approximation of acceleration in two time steps by a combination of both trigonometric cosine and hyperbolic cosine functions with weighted coefficient. The necessary formula of the present method is elaborated for integrating of the governing equation of motion in structural dynamics. The accuracy and stability of the present method are also studied. The numerical results are compared with those obtained using Newmark method, linear acceleration method, showing high effectiveness of the new method.

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References

Bathe, K. J., and Wilson, E. L. (1973), “Stability and accuracy of direct integration methods”, Earthquake Engineering and Structural Dynamics, 1, pp. 283-291.

Bathe, K. J., Irfan Baig, M. M. (2005), “On a composite implicit time integration procedure for nonlinear dynamics”, Computers and Structures, 83, pp. 2513-2524

Do Kien Quoc, Nguyen Trong Phuoc (2005), “Solving dynamic equation using combination of both trigonometric and hyperbolic cosine functions for approximating acceleration”, Journal of the Mechanical Science and Technology, 19 (special edi.), pp. 481-486.

Do Kien Quoc and Nguyen Trong Phuoc (2006), “A time step algorithm for dynamic analysis of structures due to earthquake”, Proc. of the 10th East Asia-Pacific Conf. on Structural Engineering and Construction - EASEC10, 3. Wind and Earthquake Engineering, Thailand, pp. 429-434.

Fung, T.C. (2003), “Numerical dissipation in time step integration algorithms for structural dynamic analysis”, Prog. Struct. Engng. Mater., 5, pp. 167-180.

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Received: 04-06-2020
Accepted: 04-06-2020
Published: 05-03-2011

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How to Cite

Phuoc, N. T., & Quoc, D. K. (2011). A numerical method for equation of motion in dynamic analysis of discrete structures. HO CHI MINH CITY OPEN UNIVERSITY JOURNAL OF SCIENCE - ENGINEERING AND TECHNOLOGY, 1(1), 30–39. Retrieved from https://journalofscience.ou.edu.vn/index.php/tech-en/article/view/375

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Copyright (c) 2011 Nguyen Trong Phuoc; Do Kien Quoc

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.