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Biomechanics And Motor Control Of Human Movement

Advanced Mathematical Methods for Scientists and Engineers

Nonlinear Oscillations: Exact Solutions and their Approximations

Zeros of orthogonal polynomials

Polynomials orthogonal on the unit circle

This paper deals with electrostatically actuated micro and nano-electromechanical (MEMS/NEMS) circular plates. The
system under investigation consists of two bodies, a deformable and conductive circular plate placed above a fixed, rigid
and conductive ground plate. The deformable circular plate is electrostatically actuated by applying an AC voltage
between the two plates. Nonlinear parametric resonance and pull-in occur at certain frequencies and relatively large AC
voltage, respectively. Such phenomena are useful for applications such as sensors, actuators, switches, micro-pumps,
micro-tweezers, chemical and mass sensing, and micro-mirrors. A mathematical model of clamped circular
MEMS/NEMS electrostatically actuated plates has been developed. Since the model is in the micro- and nano-scale,
surface forces, van der Waals and/or Casimir, acting on the plate are included. A perturbation method, the Method of
Multiple Scales (MMS), is used for investigating the case of weakly nonlinear MEMS/NEMS circular plates. Two time
scales, fast and slow, are considered in this work. The amplitude-frequency and phase-frequency response of the plate in
the case of primary resonance are obtained and discussed.

On electrostatically actuated NEMS/MEMS circular plates

This paper investigates the voltage-amplitude response of soft AC electrostatically actuated M/NEMS clamped circular plates. AC frequency is near half natural frequency of the plate. This results in primary resonance. The system is analytically modeled using the Method of Multiple Scales (MMS). The system is assumed weakly nonlinear. The behavior of the system including pull-in instability as the AC voltage is swept up and down while the excitation frequency is constant is reported. The effects of detuning frequency, damping, Casimir force, and van der Waals force are reported as well.Copyright © 2014 by ASME

Primary Resonance Voltage Response of Electrostatically Actuated M/NEMS Circular Plate Resonators

The paper presents comparatively the measured and estimated natural frequencies and mode shapes of a rectangular orthotropic panel. The experimental tests were performed using a shaker. The plate was fixed in horizontal position directly on the shaker armature using a rigid rod. The experimental modes shapes were visualized using sand particles. The measured natural frequencies and also the modes shapes correspond to the whole system in motion. So, the analytic model of the plate must include the effect of the vibrator connected to the plates. The purpose of this experimental measurements and analytic modeling of such plates is to further developing a methodology to estimate the material properties of the composite panels. At this research stage, an orthotropic plate with unknown material properties was investigated. Using an adequate finite element model, the mechanical properties of the material were estimated. Using these properties it is possible to numerically estimate the dynamic behavior of the plate for additional sets of boundary conditions.Copyright © 2005 by ASME

Dynamic Analysis of Composite Plates

Mass deposition influence on natural frequencies of nonuniform cantilever resonator sensors of linear and parabolic
thickness is investigated in this paper. Resonator sensitivity, defined as a fraction of change in frequency per deposited
mass, is found. Constant thickness mass deposition on all four lateral surfaces of the cantilever of rectangular crosssection
was assumed. The Euler-Bernoulli theory was used under the assumption that the beams are slender. Mass
deposition on the free end surface of the beams was neglected. The deposition thickness was considered uniform and
very small compared to any beam dimension. The deposited mass had no contribution to the stiffness, only to the mass.
Results show that when compared to the sensitivity of uniform resonator, the sensitivity of linear thickness resonator and
parabolic thickness resonator are in the first mode 6 times and 3 times higher, respectively.

On nonuniform resonator sensors

Mass deposition changes resonance frequencies of structures. Resonator sensitivity, defined as a fraction of change in
frequency per unit deposited mass, is found for microcantilever sensors electrostatically actuated to include fringe and
Casimir effects. These actuation forces produce nonlinear parametric oscillations. Constant thickness mass deposition on
all four lateral surfaces of the cantilever of rectangular cross-section was assumed. The Euler-Bernoulli theory was used
under the assumption that the beams are slender. Mass deposition on the free end surface of the cantilever was neglected.
The deposition thickness was considered uniform and very small compared to any beam dimension. The deposited mass
had no contribution to the stiffness, only to the mass. Analytical expression of the sensitivity of electrostatically
actuated uniform microcantilever resonators sensor near natural frequency is determined.

Dumitru I. Caruntu

Papers

On electrostatically actuated NEMS/MEMS circular plates

Primary Resonance Voltage Response of Electrostatically Actuated M/NEMS Circular Plate Resonators

Dynamic Analysis of Composite Plates

On nonuniform resonator sensors

On electrostatically actuated microsensors