Nonlinear analysis of electrostatically actuated diaphragm-type micropumps

摘要

Diaphragm micropumps are the most common type among indirectly driven micropumps. The elastic diaphragm is deflected using a bias voltage and then driven to vibrate around its deflected position by a harmonic AC load to produce a flow rate. This paper investigates the nonlinear resonant behavior of a circular elastic diaphragm interacting with incompressible and inviscid liquids inside a cylindrical chamber containing a central discharge opening. The governing equations of the system are derived by taking into account the nonlinear electrostatic force and fluid pressure exerted upon the diaphragm which is formulated using the linear form of Bernoulli's equation. In the modeling stage, the kinematic and compatibility conditions are incorporated into the elastic vibration of the diaphragm. The method of multiple scales is used to obtain an approximate analytical solution to the nonlinear resonant curves of the transverse oscillation amplitudes. It is shown that, as the DC voltage increases, the system exhibits softening behavior. The results also show that decreasing the discharge diameter further bends the frequency response cure to left side, which is an indication of increase in the system nonlinearity. The effects of micropump chamber height on the frequency curves were also studied and showed that softening behavior increases with decreasing chamber height. In addition, it was found that the electrical and inertial properties of the operating fluid can change the resonant curves significantly.