| Abstract: | The geophone spurious frequency is modeled as the resonance of the planar motion of a spider spring carrying a moving mass. An analytic solution is found using the Castigliano method by assuming that the spring arm is a single-mode vibrating cantilever beam. The spring shape is found from this analysis. When the typical spring has a circumferentially varying cross-section, the Castigliano method is no longer applicable. A dimensional analysis is used as an approximate method for general design. Based on the theoretical result, a rotational fixture and a translational fixture were designed for experimental purposes. A low-noise fixture and a phase-averaging technique provide the amplitude and spurious resonance in the frequency domain. Finally, a test is run by using a rotational fixture to compare with the approximate method of spurious frequency prediction. Very good agreement between prediction and experiment is found. |
