Modeling of a clamped–clamped beam vibrating in a fluid for viscosity and density sensing regarding compressibility

Modeling and simulation of a ZnO nanowire bridge and development of an electrical equivalent circuit in liquid

“…To incorporate the influence of the surrounding liquid in the electrical equivalent circuit we need to consider the additional forces that are now acting on the beam. In [12], vibrational behavior of the doubly clamped beam immersed in liquid has been investigated. Influence of the surrounding liquid on the vibrating beam has been accounted for by adding respective resistance terms to the harmonic beam equation.…”

“…The viscous damping term accounts for the pressure exerted by the surrounding fluid on the faces of the beam and the friction introduced due to the liquid. The equivalent circuit model derived in the previous section has been extended to be applicable for operation of the device in liquid based on the analysis presented in [12]. The harmonic fluid resistance, k' can be interpreted as the real part k m , representing an added mass coefficient and the imaginary part k d , representing the damping coefficient.…”

“…The resonant frequency in radians per second, of the beam in nth mode, immersed in liquid, l ω is given as [12] …”

A vibrating membrane rheometer utilizing electromagnetic excitation

“…In Ref. [11] the complex fluid resistance parameter k(ω, ρ, η) in Eq. (1) is obtained by a numerically efficient method.…”

A micromachined suspended plate viscosity sensor featuring in-plane vibrations and integrated piezoresistive readout

“…The flow field around the beam is rather complex with a significant damping due to compressional waves [5]. In contrast, sensors which mainly excite shear waves in the liquid, like the TSM resonator, feature much lower damping [3].…”