Reconstruction of Accelerations Domain on the Basis of Limited Array of Measured Accelerations and Unknown External Force Excitation

Abstract

During the operation of engineering structures, in some cases on the basis of the results of measurements of kinematic parameters – accelerations at individual points of the structure or angular accelerations – may the need rise to determine these parameters over the entire structure. In addition, the problem of estimating the external force that caused the dynamic response of the structure is of interest. In cases where the point of application of the external force is known, its magnitude and time history can be determined effectively. This paper addresses a more complex problem: determining accelerations over the entire elastic structure when both the point of application and the time dependence of the external force are unknown, based on acceleration measurements at a limited number of points on the structure. The problem of identifying the location and time-dependent function of the external force is also considered. The solution is based on representing the unknown external force as a complex Fourier series with unknown coefficients and minimizing the discrepancy between the measured and calculated accelerations.