Acta Mechanica Sinica

, Volume 4, Issue 2, pp 156–164 | Cite as

An unconditionally stable calculation scheme for the dynamic response of structures by the method of spline collocation

  • Lin Wenjing
  • Xu Cida


In this paper, by the method of collocation, using the cubic β-spline function as the trial function in the time domain and putting zero residuals of the differential equation of motion of the structure at two points of time, the authors obtain an unconditionally stable calculation scheme for the dynamic response of the structure. When a parameter σ in the scheme is within the interval 0.15<σ <0.5 the scheme is absolutely stable. It is shown that the accuracy of the scheme, as may be measured by AD (the decay of the amplitudes), PE (the elongation of periods) and the algorithmic damping ratio, is better than that of traditional methods—the Wilson-σ's method, the Newmark's method and the Houbolt's method. A numerical example is given in which a certain dynamic response problem is solved by the method of this paper and results are compared with that of the traditional methods and the analytic method showing that the accuracy of the method by this paper is superior to the other ones. The computational scheme for the dynamic response of structures by this paper may be regarded as an effective, convenient and accurate method for dynamic response of structures.

Key Words

dynamic response spline function calculation scheme 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Houbolt, J.C.,Journal of Aeronautical Science,17 (1950), 540–550.MathSciNetGoogle Scholar
  2. [2]
    Newmark, N.M.,ASCE, Journal of Engineering Mechanics Division,85 (1959), 67–94.Google Scholar
  3. [3]
    Bath, K.J. & Wilson, E.L.,International Journal of Earthquake Engineering and Structural Dynamics,1 (1973), 283–291.Google Scholar
  4. [4]
    Bath, K.J. & Wilson, E.L., Numerical Methods in Finite Element Analysis, Prentice-Hall, Inc. Eaglewood Cliffs New Jersey U.S.A. (1976), 348–355.Google Scholar
  5. [5]
    Li Yuesheng & Qi Dongxu, Methods of Spline Functions, Science Publishing House (1979) (in Chinese).Google Scholar
  6. [6]
    Sun Huanchun,Acta Mechanica Sinica,2 (1981), 153–164 (in Chinese).Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1988

Authors and Affiliations

  • Lin Wenjing
    • 1
  • Xu Cida
    • 1
  1. 1.Department of Engineering MechanicsTongji UniversityShanghai

Personalised recommendations