A two-dimensional analysis of spurious compressional wave excitation by thickness-shear-mode resonators

Abstract

In this article we investigate the spurious excitation of compressional waves by thickness-shear-mode resonators, which are commonly used for chemical sensing and viscosity sensing. In particular, we consider the excitation mechanism due to the nonuniform shear displacement present at the sensitive surface of the resonator. To illustrate the basic mechanism we analytically develop a general solution for a two-dimensional model describing the displacement and the pressure distribution in the liquid obtained in terms of Fourier integrals. We discuss these solutions and derive a useful approximation for the far field representing said compressional modes. We finally illustrate the results considering a practical example and associated numerical results.

Verwendung piezoelektrischer Resonatoren für die Online-Messung der Dichte und Viskosität von Flüssigkeiten

“…The disturbing effect of spurious out of plane waves in connection with thickness shear resonators has been also recognized and investigated by other authors, e.g. (Martin, Hager 1989;Lin, Ward 1995;Schneider, Martin, 1995;Lucklum, Schranz et al, 1997;Jakoby, Scherer et al, 2003;Beigelbeck, Jakoby, 2004). For mathematical analysis the three layer thickness shear resonator again can be reduced to a two layer equivalent model, in analogy to the concept shown in Fig.…”

Modeling of the fluid-structure interaction in a fluidic sensor cell

“…2. The displacement amplitudes are in the range of a few micrometers, which follows both from theoretical analysis and optical measurements with a laser-vibrometer, so that the equations describing the fluid motion become linear-which is permissible for the problem where no (convective) net flow is involved [20]. This allows to obtain the three-dimensional velocity field by scaling and superposition of the two solutions.…”

Condition monitoring of viscous liquids using microsensors

“…A suitable method considered is the implementation of Euler Bernoulli beam theory by introducing a distributed load along the beam, which represents the interaction with the liquid and thus depends on the transversal motion of the beam given by its lateral displacement wðx; tÞ . It can be shown (Beigelbeck, Jakoby, 2004) that for the calculation of the interaction between beam and liquid, the Navier-Stokes equations can be linearized if the displacement amplitudes in the liquid are sufficiently small. Using complex time-harmonic notation, the distributed load due to interaction with the liquid at some position x along the beam can be linearly related to the displacement amplitude at x by means of a complex-valued coefficient (''mechanical impedance'').…”

“…Known issues in the design of shear-mode devices include spuriously excited compressional waves (Martin, Hager, 1989;Thalhammer et al, 1997;Beigelbeck, Jakoby, 2004), which may lead to disturbing interferences upon reflections from nearby obstacles as, in contrast to shear waves, compressional waves are scarcely damped even in viscous liquids.…”