A finite-element analysis on the free vibration of Japanese drum wood barrels under material property uncertainty

Abstract

This paper presents a finite-element analysis on the free vibration of Japanese drum wood barrels under insufficient material property data. Unlike isotropic material such as steel, wood behaves like an orthotropic composite material, whose elastodynamic characterization in a cylindrical shell needs Young's modulus in the longitudinal (in-grain) and circumferential (cross-grain) directions, shear modulus, and Poisson ratios. Due to measurement difficulty encountered during the process of testing, only the longitudinal Young's modulus and the specific gravity of the wood were measured. In the analysis, the finite-element models of the drum were constructed using conical shell elements. The required unknown elastic constants were estimated consecutively by a try-and-error approach, and the estimated values were reached when the computed resonance frequencies matched simultaneously with those of the seven lower modes measured in experiments. In order to accomplish this, both the estimated constants and the finite-element analysis must be within acceptable range of accuracy. It was found that the values 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 now be used for updating the finite-element model. The updated model can then be used calculating the higher order modes which cannot be practically obtained through measurements.

Elastic Constants of Polymeric Fiber Composite Estimation Using Finite Element Method

“…To verify that the results are correct, a theoretical model was also studied, obtaining a good agreement with the experimental results. To determine the properties of some materials when insufficient data are available, such as the determination of the mechanical properties of some wood species, a finite element analysis is proposed in [27]. Wood is an orthotropic material, so it is necessary to know the Young's modulus in two directions, as well as the shear modulus and Poisson's ratios.…”

Estimation of Axial Young’s Modulus of Fibrous Composites Using Finite Element Analysis

“…Modeling using a classic model confirms the accuracy of the results obtained. The FEM is also used to determine the mechanical properties of some types of wood, a situation in which there are insufficient data to describe the model and approximations at the model level are needed [30]. Things become more complicated in such an analysis since wood is an orthotropic composite, so it is necessary to know several parameters to describe the constitutive law of the material.…”

Finite-Difference model of mode shape changes of the Myanmar pat wain drum circle using tuning paste

“…The influence of non-uniform tension of a drum head was studied using laser-interferometry measurements, where degenerated modes have been found [12] mostly leading to musical beats. The eigenmodes of the drum vessel were analyzed using FiniteElement methods [3]. The coupling between the drum head and the wooden shell was investigated using Finite-Elements for a bass drum [1].…”