구조물 진동.소음의 수치해석시 최적 요소크기는 .lambda./4이다.

Optimum mesh size of the numerical analysis for structural vibration and noise prediction

An engineering goal in vibration and noise professionals is to develope quiet machines at the preliminary design stage, and various numerical techniques such as FEM, SEA or BEM are one of the schemes toward the goal. In this paper, the research has been focused on the sensitivity effect of mesh sizes for FEM application so that the optimum size of the mesh that leads to engineering solution within acceptable computing time could be generated. In order to evaluate the mesh size effect, three important parameters have been examined : natural frequencies, number of modes and driving point mobility. First, several lower modes including the fundamental frequency of a 2-D plate structure have been calculated as mesh size changes. Since theoretical values of natural frequencies for a simple structure are known, the deviation between the numerical and theoretical values is obtained as a function of mesh size. The result shows that the error is no longer decreased if the mesh size becomes a quarter wavelength or smaller than that. Second, the mesh size effect is also investigated for the number of modes. For the frequency band up to 1.4 kHz, the structure should have 38 modes in total. As the mesh size reaches to the quarter wavelength, the total count in modes approaches to the same values. Third, a mobility function at the driving point is compared between SEA and FEM result. In SEA application, the mobility function is determined by the modal density and the mass of the structure. It is independent of excitation frequencies. When the mobility function is calculated from a wavelength to one-tenth of it, the mobility becomes constant if the mesh becomes a quarter wavelength or smaller. We can conclude that dynamic parameters, such as eigenvalues, mode count, and mobility function, can be correctly estimated, while saving the computing burden, if a quarter wavelength (.lambda./4) mesh is used. Therefore, (.lambda./4) mesh is recommended in structural vibration analysis.