Measurement of Chladni Mode Shapes with an Optical Lever Method

This procedure can provide a clear glance for determining the Chladni mode shape using the optical lever method. The proposed method is a rather simple approach to quantitatively determine the Chladni mode shape at a very low cost. Knowledge of the partial differential equation and the finite element method is important for successful execution of the procedure.

To set up the vibration system, acquire two 1mm thick mirrored circular acrylic plates with 150mm diameter and 200mm diameters respectively. Drill a 3mm diameter hole in the center of each plate, and mark several points every 5mm along an arbitrary radius. Attach each plate to the actuate bar of the vibrator with a bolt in the middle point, and use a waveform generator to drive the vibrator with a sine wave.

To acquire the resonance frequency, use the laser pen to perpendicularly project the laser beam from a 120mm distance onto the vibrating plate, such that the beam is reflected to the light screen 500mm in the distance. Quickly move the laser pen along the direction perpendicular to its length to scan over the diameter, while the signal generator continuously changes its frequency. When the spot length is significantly stretched along the diameter, and some spots with almost no expansion appear, begin scanning the certain frequency range slowly, and determine the frequency at which the spot expands most obviously.

To prepare the light path and measurement system, place the light screen parallel to the vibrating plate, and mark the distance with a meter ruler. Then, using 500mm as the starting distance, place the laser pen to project the beam perpendicularly onto the plate, such that the beam is reflected to the light screen in the distance, making sure that the previously made mark can be scanned while the laser pen is moving. To obtain an experimental measurement, turn on the signal generator, and set the excitation frequency to the resonance frequency at which the spot expanded most obviously.

The signal intensity should be as small as possible once the light spot on the light screen is large enough to be recorded. Adjust the laser pen such that the incident point coincides with the first marker, that is, with the nearest marker to the fixed point of the plate, and move the screen from 500mm to 1000mm, measuring the spot length from the screen every 50mm. Then adjust the laser pen to make the incident point adjacent to the next marker, and repeat the measurements from 500mm to 1000mm as just demonstrated.

When all of the incident points have been measured, repeat the measurement with the acrylic plate of the next largest diameter. The excitation frequency that can excite an axisymmetric Chladni pattern is determined through the frequency sweeping test. A larger plate diameter correlates with a higher plate flexibility.

Under the corresponding resonant frequency, the length of the light spot on the light screen of different plates can be measured and recorded. Plotting this data allows comparison of the mode shapes of different plates. The most important aspect of this procedure is obtaining accurate data when measuring the spot length, as this data determines the accuracy of the entire experiment.

This method can also be used to determine non-axisymmetric mode shapes in word minor, to diamonds trace the beauty of Chladni patterns.