Narrow-band chirp test as a method for determining resonant frequencies in Chladni plates

Abstract

Chirp tests are commonly used to measure the frequency response of systems. The frequency range of the chirp signal is often chosen to encompass the possible frequencies at which the system is expected to resonate. However, in this study, we show that a narrow-band chirp of low frequencies can detect resonant frequencies beyond the range. By applying the chirp signal to a 200 mm x 200 mm x 1 mm aluminum Chladni plate, the frequency response of the recorded vibration showed peaks at frequencies 108 Hz, 271 Hz, 539 Hz, 828 Hz, and 1328 Hz. A refinement process is made by examining the particle's motion at frequencies around the initially detected peaks to look for the exact frequency at which the beads exhibited the most significant movement. After the refinement process, the actual resonant frequencies of the plate were determined to be 105 Hz, 272 Hz, 545 Hz, and 833 Hz. However, no movement is observed at and around 1328 Hz. The corresponding resonant wave numbers k for the plate is numerically determined to be 1.4060 [πa⁻¹], 2.4653 [πa⁻¹], 3.4347 [πa⁻¹], and 4.2436 [πa⁻¹]. Through linear regression analysis of the f_exp and k², the experimental constant C_exp was determined to be 0.1872 m²/s with R² = 0.9998. Numerical simulations using the derived C_exp showed good agreement with the experimental Chladni patterns.