Subharmonic Resonance of Two Thirds Order of Electrostatically Actuated Bio-MEMS Circular Plates: Amplitude-Frequency Response

This paper deals with subharmonic resonance of two thirds order or electrostatically activated BioMEMS circular plates. Specifically, this paper investigates the frequency amplitude response of this resonance. The system consists of a clamped flexible circular plate above a parallel electrode situated at a distance, and under an AC voltage of frequency near three fourths of the natural frequency of the plate. The method of multiple scales is used to model the hard excitations in the system, hard excitations that are necessary to produce this secondary resonance. This work predicts the response, as well as the effects of parameters such as voltage and damping on the response. This paper predicts that the subharmonic resonance of two thirds order consists of a near zero steady state amplitude, and higher values steady state amplitudes consisting of a stable branch and an unstable branch, and a saddle-node bifurcation point. The predictions regarding the effects of voltage and damping on the response of the BioMEMS plate shows that as the voltage increases, the bifurcation point is shifted to lower frequencies and lower amplitudes, while as the damping increases the bifurcation point is shifted to lower frequencies and high amplitudes. Therefore, the increase of damping leads to a case in which it is harder to reach higher amplitude steady-state solutions since it requires large initial amplitudes of the plate.

ROM of Voltage Response of Parametric Resonance of Electrostatically Actuated MEMS Plates

This paper deals with electrostatically actuated Micro-Electro-Mechanical Systems (MEMS) circular plates. The system consists of a flexible circular plate with the edge fixed above a parallel ground plate. The forces acting on the MEMS plate are the electrostatic, damping, and elastic restoring force. In this work Casimir and/or van der Waals forces are neglected, since they are significant for gaps less than one micron and/or 50 nanometers, respectively. The electrostatic force is given by a soft Alternate Current (AC) harmonic voltage between the two plates. The electrostatic force leads the flexible plate into vibration. The assumption of axisymmetrical vibrations is valid in this work. The AC frequency is near natural frequency of the flexible circular plate. Since the electrostatic force is proportional to the square of the voltage, this results in an electrostatic force of frequency twice the natural frequency. Therefore the system experiences a parametric resonance. The partial differential equation of motion is non-dimensionalized. Next the resulting lumped parameters are found from a typical MEMS circular plate resonator. Reduced Order Model (ROM) is the method of investigation used in this work, specifically two terms ROM. Numerical simulations are conducted to predict the voltage response of the system. The effects of frequency and damping on the response are predicted as well. MEMS circular plate systems are excellent candidates for resonator sensors, i.e. sensors functioning at resonance. They are capable of detecting cells, viruses, as well as any microparticles provided the plates are coated for such recognition.

Analysis of a Low Speed Flexible Flat Land Thrust Bearing

The problem of a flexible flat land thrust bearing is studied here. The bearing consists of a flexible circular plate running against a rigid flat surface. Point loads are applied to the plate at equally spaced locations causing deflection of the plate. The deflection of the plate creates the converging clearances necessary for hydrodynamic lubrication. The fluid film between the disk and the plate is treated as incompressible. Results are presented in terms of normalized variables enabling the design of a broad range of bearings based on this mechanism.

The Dynamics of a Gyroscope Supported by a Flexible Circular Plate

The dynamics of a rigid rotor supported on a flexible circular plate is investigated and it is shown that the arrangement is capable of operating as a tuned free rotor gyroscope. The performance characteristics of the gyroscope are evaluated and the analysis shows that the steady displacment of the rotor may be used to measure either the angular velocity or angular displacement of the supporting casing. For both modes of operation the free motion and the response to a constant rate and a vibratory input is determined.