THEORETICAL DISCUSSION ON ERRORS IN THE NEWMARK METHOD : In the case of dynamic responses during earthquakes

Abstract

Newmark explained the theory of errors in the Newmark method in the case of free vibrations that the errors were caused by the difference between the differential eauation in actual vibrations and the difference equation in numerical analyses of vibrations. In the present study the above theory of errors is applied to the analyses of dynamic responses to earthquake excitations. The result shows that the dynamic responses of theoretical numerical analyses for parameter β=O reoresent the actual phenomena with small error, while the error is larger when the value of β is larger. If the value of β except 0 is wanted to use, the time interval must be very small. The present theoretical analyses and the result of numerical analyses exhibit good agreement.