Abstract
Numerical simulations were carried out using the Finite Element Method (FEM) to determine the frequency characteristics of mechanical vibration of diatom silica frustules under the conditions and at frequencies that are not readily accessible to experimental measurement. The results revealed the influence of the frustule morphology on the natural frequency spectra. The effect of frustule density, stiffness, dimensions, pore size, and wall thickness on the eigenfrequencies and the corresponding modal shapes were studied in detail. Diatom frustules have natural frequencies in the range between several MHz and tens of MHz that make them a promising candidate for future MEMS applications. Eigenfrequencies depend linearly on the speed of sound in the frustule wall and decrease parabolically with the diameter and the pore size to diameter ratio. Dimensional analysis allowed obtaining functional correlations that encapsulate the various dependencies in compact analytical form. The satisfactory nature of our calculations and correlations derived from them is confirmed through an agreement with the analytical solutions from the literature.
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