Miniaturized micro-electro-mechanical systems (MEMS) loudspeakers is a current developmental trend for in-ear audio applications. However, when a loudspeaker shrinks to a size of a microelectronic chip, the involved physics starts to differ from the macroscopic world. At one side, an electrostatic µSpeakers benefits from small electrode gaps leading to high driving forces. At the same time, the fluid dynamics of the air can cause strong damping forces inside the microscopic cavities of a MEMS loudspeakers chip. Recently we have shown experimentally that the first Euler-Bernoulli bending mode is sufficient to reproduce the behavior of a Coulomb-actuated microbeam over the entire stroke with high accuracy. This leads to an ab initio modeling approach based on a novel Chebyshev-Edgeworth type expansion that leads to an accurate lumped parameter model (LPM) with a single degree of freedom for MEMS loudspeakers. In this work, we discuss the influence of microfluidics on the damping of a balanced nanoscopic electrostatic drive (NED) test loudspeaker design. With the help of the finite element method (FEM) we analyze how the pressure and velocity distribution is linked to the Euler-Bernoulli modes of a simple micro-beam, with the aim of including the squeeze film damping in the LPM. Understanding the various sources of fluid dynamic damping is of great importance for the design of high fidelity MEMS based electrostatic audio transducers (μSpeakers).
A recently introduced new CMOS compatible actuator class, called nano electrostatic drive (NED), uses electrostatic actuation to provide significant deflections of elastic structures. The behavior of such actuators can be dominated by nonlinear phenomena, if the nonlinearities are not understood and not considered in the design. One of the main nonlinearity sources is the electrostatic actuation, which results in the well-known instability named pull-in. Additionally, due to large deflections provided by NED technology, stress stiffening and large deformation significantly influence the system, shifting the eigenfrequencies, altering the pull-in voltage, or even introducing geometrical buckling. All these effects together characterize static and dynamic behavior and can be tailored to partially counterbalance each-other by specific designs. In following, we use finite element method (FEM) to analyze the static and dynamic behavior of MEMS based on NED technology. Owing to coupled-field FEM technique, we observe effects like static pull-in, electromechanical eigenfrequency shift and transient phenomena in detail. The numerical results are validated during optical experiments, which supports the conclusions arose from the FEM. Finally, characterizing of the nonlinearities grants the ability to tailor and minimize them during the MEMS design process.
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