Modeling of Disturbance Parameters Influence on a Dual-Channel Piezoelectric Gravimeter Operation

Abstract

The work is devoted to the problem solving of study of the influence of both perturbing accelerations parameters and the inherent parameters of a dual-channel piezoelectric gravimeter on its operation, by means of a computer. For this purpose, a mathematical model of a dual-channel piezoelectric gravimeter was used. In consequence of the carried out mathematical model modeling, the results of modeling on a computer are obtained and presented. The influence of the external disturbance parameters on a new dual-channel piezoelectric gravimeter operation was modeled. As external disturbances, the following was considered: influence of both frequencies and amplitudes of forced vibrations of the base (along longitudinal and transverse axes), on which a dual-channel piezoelectric gravimeter is located, as well as the disturbing vibration accelerations for the most unfavorable resonance cases: w = w₀, w = 2w₀, w = 3w₀, 2w = w₀, 3w = w₀, where w₀ — is the natural vibration frequency of a dual-channel piezoelectric gravimeter, w - is the disturbances frequency. In consequence of the carried-out modeling, the graphs of the output signal change were obtained for various values of the disturbance frequency of vibration accelerations, the damping coefficient and various values of the disturbing vibration accelerations amplitudes. In view of each result and graph that have obtained, the analyzes as to the steady-state forced vibrations magnitude of a two-channel piezoelectric gravimeter as well as the conclusion concerning presence or absence of resonance were made. Using the results of previous studies of the authors, the comparison of the analytical solution of the equations of a dual-channel piezoelectric gravimeter motion, when exposed to the external disturbances was carried out with the results of digital modeling. The analysis of the modeling results has shown that the mean root square deviation of the solutions does not exceed 0.009 mm and this analysis has confirmed the adequacy of the mathematical model of a two-channel piezoelectric gravimeter, in other words, the obtained mathematical model of a dual-channel piezoelectric gravimeter corresponds to a real device and this model can be used for further studies of a dual-channel piezoelectric gravimeter motion parameters.