Sound dissipation from plate-type resonators excited in non-conventional transversal modes in liquids

Abstract

Vibrational modes of higher order in micromachined resonators exhibit low damping in liquid environments, which facilitates accurate sensing even in highly viscous liquids. A steady increment in mode order, however, results in sound dissipation effects at a critical mode number n(crit), which drastically increases damping in the system. Basic understanding in the emerging of sound dissipation in micromachined resonators is therefore of utmost importance, when an application of higher mode orders is targeted. For that reason, we experimentally investigated in this paper the appearance of sound dissipation in higher order non-conventional vibrational modes in MEMS plate resonators in liquids. The results are compared to those of an analytical model and of finite element method analyses. Micromechanical piezoelectric resonators were fabricated and characterized in sample fluids with a dynamic viscosity μ(fluid) ranging from 1 to 5 mPa s and density values ρ(fluid) ranging from 0.774 up to 0.835 kg l⁻¹. Quality factors up to 333 are obtained for the eighth mode order in model solution with a dynamic viscosity of 1 mPa s. By monitoring the resonance and damping characteristics as a function of mode order, sound dissipation effects occur, observed by the detection of increased damping, starting at mode number n = 8, which is in good agreement to the predictions of an analytical model and to finite element method simulations. At the critical mode number n crit, a reduction in quality factor up to 50% is measured. The results show a direct correlation of n crit and the density of the fluid, which agrees to theory. The lowest value of 8 for n(crit) is obtained in a sample liquid with the lowest density value of 0.774 kg l⁻¹, followed by n_(crit) = 9 in a sample liquid with ρ_(fluid) = 0.782 kg l−1 and n(crit) = 10 in a sample liquid with ρ_(fluid) = 0.835 kg l⁻¹. These findings are of particular interest for sensing applications in low dense liquids, as sound dissipation effects emerge even at lower mode numbers.

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