COMPOSITIONS OF TIME HISTORIES OF ACCELERATION AND VELOCITY AND DISPLACEMENT OF GROUND MOTION

The compositions of time histories of acceleration, velocity and displacement of ground motion are studied. The acceleration time history of ground motion is represented as sine series. The formula for calculating the velocity time history composed of the general term of velocity is yielded by integrating the sine series. The formula for calculating the displacement time history composed of the general term of displacement is developed by integrating the velocity time history obtained above. The acceleration time histories of Landers, Taft and El-centro waves in PEER database are selected. The acceleration, velocity and displacement time histories of these three seismic waves are calculated by using the formulas given in this paper. The correctness of the formulas is verified by comparing the calculated time histories respectively with the corresponding acceleration, velocity and displacement time history provided by the database. The general term of acceleration, general term of velocity and general term of displacement are obtained. The acceleration, velocity and displacement time histories of ground motion are composed of the summation of general terms of acceleration, velocity and displacement respectively.