Prediction of the Square Plate Natural Frequency by Using the Mean Wavelength of the Actual Nodal Lines and the Modal Overlap Factor

Authors: Barenten Suciu, Sota Karimine

Abstract:

In this paper, photos of the nodal lines forming on plates made in copper and bronze in the range of low frequencies are shown in correlation with the recorded vibration spectra. Resonant peaks corresponding to the rigid plate mode of vibration, as well as the lowest bending plate mode of vibration, are identified. Then, the damping ratio at these resonant frequencies is evaluated by using the Q-factor technique. In order to achieve agreement between the predicted and measured frequencies, the mean wavelength is accurately evaluated by taking into account the rounding of the actual nodal lines near the plate edges. Additionally, a frequency correction factor multiplying the core of the frequency expression is introduced to precisely fit the measured values of the frequency. The relationship between the proposed frequency correction factor and the well-known modal overlap factor is explicitly illustrated. In this way, a reliable model able to correlate the excitation frequency with the shape of the actual nodal lines can be achieved, and based on it, control of the micro-particles motion on the vibrating plates via frequency adjustment can be successfully implemented.

Keywords: Nodal lines shape control, frequency adjustment, frequency correction factor, modal overlap factor, square metallic plates.

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