Identification of beat characteristics and damping ratios of bell type structures using wavelet transform

The aim of this paper is to propose an effective method for extracting the beat characteristics and modal damping ratios of the bell type structures using the continuous wavelet transform (CWT). The bell type structures which can be simplified as a slightly asymmetric circular ring and cylindrical shell are commonly used to analyze those of a Korean bell. The beat response is caused by the mutual interference of mode pairs, which are created by the slight asymmetry of the bell type structures in the circumferential direction. First of all, the beat frequencies and periods of each vibration mode are obtained using the CWT based on the Gabor wavelet. Next, the modal damping ratios associated with the time duration of the beat response are also extracted by the CWT. When using the CWT on a given signal, the optimal shape of the Gabor wavelet used as the mother wavelet is determined by employing the Shannon entropy cost function on the normalized wavelet modulus. In order to show the accuracy of the proposed method, the beat characteristics and damping ratios are extracted from the simulated pure and noisy signals, which have mode pairs. Finally, the proposed method is applied to a small-sized Korean bell to verify its applicability in the field.