Studies on the vibration of Japanese drum wood barrels under material property uncertainty

Abstract

Unlike isotropic material such as steel, wood behaves as a highly orthotropic composite material. Due to measurement difficulty, only the longitudinal Young's modulus and the specific gravity of the wood were successfully measured at the time the wood barrel was made. In the experiments, mode shapes and modal resonance frequencies were measured. In the numerical modal analysis, the finite-element model of the drum was constructed using orthotropic conical shell elements which require more elastic constants than those being measured. A try-and-error method was used to estimate those unknown constants by comparing the computed and measured modal frequencies and shapes. It was found that the estimated value of the circumferential (cross-grain) Young's modulus, which was unknown at the beginning of the study, turns out to be crucial in determining the lower mode resonance frequencies. The usefulness of this analysis is that the estimated elastic constants can be used for updating the finite-element model which can then be used for calculating the higher order modes. These higher modes cannot be practically determined by measurements. [Work by 2nd author supported by Miyamoto Unosuke Shouten Co.]