MODEL STUDIES OF THE VIBRATIONS OF STRUCTURES DURING EARTHQUAKES, BASED ON GROUND ACCELERATIONS INSTEAD OF ON GROUND DISPLACEMENTS* By MERIT P. WHITE and RALPH BYRNE

ONE OF the most important problems in the field of earthquake engineering deals with the dynamics of structures. Any building is an elastic system. As such, its deflections (stresses) during an earthquake may depend on its own dynamical characteristics as well as on the nature of the ground motion. An ordinary building is a relatively complicated dynamic system, usually of many degrees of freedom and with considerable internal friction. The treatment of this problem may be simplified by the assumption that this internal friction is equivalent to viscous damping. 1 A further simplification results from first treating systems of one degree of freedom, combining these results if the behavior of a more complicated system is desired. Although very useful conclusions can be drawn with no knowledge of actual ground motions, nevertheless the most valuable results will be based on records of actual earthquakes, such as the accelerograms recently" obtained in California and Montana by the United States Coast and Geodetic Survey. The response of a given oscillator to a particular disturbance may be obtained analytically or experimentally. The usual, in fact to date the only, experimental procedure has been to subject the oscillator model to a base displacement corresponding to the one being studied. Analytical calculations of the response, on the other hand, can be based on ground accelerations or velocities as well as displacements. This fact has given a certain advantage to the analytical approach, since the principal records of severe ground motions are acceleration records which must be double-integrated if displacements are desired. However, it is possible to carry out model studies of linear, one degree of freedom oscillators with or without viscous damping, using only ground accelerations. This paper describes the general procedure which must be followed and gives the argument justifying this process. Consider first a simple, undamped, linear oscillator consisting of a mass on a flexible support whose base is being accelerated at the rate j. We introduce the following expressions used in the equations below: