Mathematical Theorem of Mode Acceleration Method

모우드 가속도법의 수학적 정리(定理)

  • 김태남 (상지대학교 토목공학과)
  • Published : 2003.04.01


Mode superposition method(MSM) is the most commonly used for solving linear response problems of structural dynamics. The major advantage of MSM is that usually a small number of lower mode is sufficient to analysis the response. However, the convergence is slow and many modes would be needed to give an accurate MSM in large structure with many degrees of freedom. The inaccuracies of MSM are caused by mode truncation in the solution. These demerits can be overcome by use of the mode acceleration method(MAM). Example analyses are carried out in simple beam subjected to harmonic loadings and compared the convergence of the joint displacements by the two methods. For relatively low frequency loadings, a good results was obtained by the lowest one mode in MAM, so the method is more economic in numerical analysis on an accurate solution.


  1. Cornwell, R., Craig, R. R., and Johnson, C. P., “On the application of the mode-acceleration method to structural engineering problems,” Earthquake Engineering and Structural Dynamics, Vol. 11, 1983, pp. 679-688.
  2. Paz, M., Structural Dynamics : Theory & Computation, Van Nostrand Reinhold Company, 1985, p. 561.
  3. Anagnostopoulos, S. A., “Wave and earthquake response of offshore structures : Evaluation of modal solutions,” J. of Structural Division, ASCE, Vol. 108, No. ST10, 1982. 10, pp. 2175-2191.
  4. Clough, R. W. and Penzien, J., Dynamics of Structures, McGraw-Hill, 1975, p. 634.
  5. Leger, P., and Wilson, E. L., “Modal summation methods for structural dynamic computations,” Earthquake Engineering and Structural Dynamics, Vol. 16, 1988, pp. 23-27.
  6. 이인원, 이종원, 정길호, “대형구조물의 모우드 해석 방법”, 대한토목학회논문집, 제13권, 제5호, 1993. 11, pp. 77-83.
  7. Kreyszig. E., Advanced Engineering Mathematics(4th edition), John Willey & Sons, 1976, p. 937.
  8. Craig, R. R., Structural Dynamics; An Introduction to Computer Methods, John Willey & Sons, 1981, p. 527.