Physical modeling of Japanese temple bells using thin cylindrical shells involving dynamics of clappers <i>Shumoku</i>

In this paper, we present a physical model of Japanese temple bells based on the elasticity theory thin cylindrical shells. The proposed involves dynamics clapper, called shumoku, thereby constructing total system bell. governing equation bell is solved semi-analytically using Fourier series expansion in circumferential direction. finite difference method (FDM) applied to axial These modeling and numerical treatment are an attempt reduce computational costs while retaining essence bells. Shumoku physically modeled as 3D beam, numerically analyzed by element (FEM). Simulation results show that fundamental frequencies calculated close those existing FDM calculations measured data, differences higher-order partial observed, indicating attributed details structural features omitted model. Changing material shumoku affects spectrogram vibration bell, suggesting importance clappers precisely simulate systems.