COMPARISON OF NUMERICAL METHODS FOR ANALYZING THE DYNAMIC RESPONSE OF STRUCTURES
Abstract
The analytical treatment is based on the general theory of the calculus of difference equations and the algebra of matrices. In ordinary problems of vibratory motion, Newmark's Beta(coefficient measuring the proportion of acceleration at the end of an interval in determination of displacement) method (MIT Conference on Building in the Atomic Age, June 16, 1952) is valuable because of flexibility in application. The choice of time interval may be made for the desired rate of convergence and accuracy by adjustment of the Beta parameter. The linear acceleration method, a special case of the Beta method for Beta = 1/6, is most consistent in degree of error when the motion is that of forced vibration with damping, with initial displacement and velocity. Timoshenko's method (Vibration Problems in Engineering, 2nd ed., D. Van Nostrand Co. Inc., New York, 1937) is best applied to an undamped system when the response in amplitude is important. The constant acceleration method and Euler's method are not advisable because of their inaccuracy. If the masses in motion are not damped and have no initial velocity, Salvadori's method (J. Amer. Concrete. Inst. 23, no. 1:Sept. 1951) is rapid and accurate. For rapid and less accurate work, Levy's method (NBS 2410) may be used, but care should be taken in the treatment of initial velocity. Runge and Kutta's methods, discussed in Levy and Baggott (Numerical Solutions of Differential Equations, Dover Publications Inc., New York, 1950), are accurate and general in application, but their procedure is tedious.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 20, 1952
- Accession Number
- AD0004106
Entities
People
- N. M. Newmark
- S. P. Chan
Organizations
- University of Illinois Urbana–Champaign