SIMPLE METHOD OF IDENTIFICATION OF THE TWO INTEGRATION CONSTANTS FOR THE NUMERICAL DOUBLE INTEGRATION OF ACCELERATION

This paper is intended to be a clarification, a technical support for those who might have difficulties when integrating twice the accelerations in order to obtain correct displacements, consistent with reality. Since the mounting of the displacement sensors on the dynamic system is not always easy, the possibility of obtaining the displacements from acceleration measurements which are usually much more affordable represents an interesting option. There are two possibilities: integrating analogically the accelerations using a performing data acquisition system (accelerometer, amplifier, oscilloscope), or the numerical double integration of the acceleration. This numerical integration is detailed here, presenting a simple searching method for determining the two a priori unknown integration constants Cx(t0) and Cv(t0) of the integration formula. Two practical case studies are illustrating the method for identifying these two integration constants. The second case study concerns the impact of a flat sample material with an impactor head.