On the Wavelength and Frequency of the Actual Chladni Patterns Visualized on Square Plates

In this study, Chladni patterns are visualized on square plates made of various metallic materials in the domain of low frequencies around the first flexural resonant peak. Using the membrane and the thin plate models, the undamped and damped natural frequency of the square panel is explicitly expressed versus the mean wavelength of the bending vibration. The wavelength of the idealized Chladni figures is evaluated for linear and curvilinear nodal lines relevant to our experiments. Significant discrepancy between the computed and measured frequencies is corrected based on the wavelength evaluation of the actual Chladni figures, done by considering the cutting and rounding of the nodal lines near the plate edges and near the central point of excitation. Such model able to link the shape of the actual nodal lines with the excitation frequency is useful for the motion control of micro-particles on the vibrating plate.