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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 uses the reduced order model (ROM) method to investigate the nonlinearparametric dynamics of electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators under soft alternating current (AC) voltage of frequency near half natural frequency. This voltage is between the resonator and a ground plate and provides the actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as a Euler-Bernoulli cantilever. ROM convergence shows that the five terms model accurately predicts the steady states of the resonator for both small and large amplitudes and the pull-in phenomenon either when frequency is swept up or down. It is found that the MEMS resonator loses stability and undergoes a pull-in phenomenon (1) for amplitudes about 0.5 of the gap and a frequency less than half natural frequency, as the frequency is swept up, and (2) for amplitudes of about 0.87 of the gap and a frequency about half natural frequency, as the frequency is swept down. It also found that there are initial amplitudes and frequencies lower than half natural frequency for which pull-in can occur if the initial amplitude is large enough. Increasing the damping narrows the escape band until no pull-in phenomenon can occur, only large amplitudes of about 0.85 of the gap being reached. If the damping continues to increase the peak amplitude decreases and the resonator experiences a linear dynamics like behavior. Increasing the voltage enlarges the escape band by shifting the sweep up bifurcation frequency to lower values; the amplitudes of losing stability are not affected. Fringe effect affects significantly the behavior of the MEMS resonator. As the cantilever becomes narrower the fringe effect increases. This slightly enlarges the escape band and increases the sweep up bifurcation amplitude. The method of multiple scales (MMS) fails to accurately predict the behavior of the MEMS resonator for any amplitude greater than 0.45 of the gap. Yet, for amplitudes less than 0.45 of the gap MMS predictions match perfectly ROM predictions. [DOI: 10.1115/1.4023164]

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

This paper deals with the nonlinear response of electrostatically actuated cantilever beam microresonators near-half natural frequency. A first-order fringe correction of the electrostatic force, viscous damping, and Casimir effect are included in the model. Both forces, electrostatic and Casimir, are nonlinear. The dynamics of the resonator is investigated using the method of multiple scales (MMS) in a direct approach of the problem. The reduced order model (ROM) method, based on Galerkin procedure, is used as well. Steady-state motions are found. Numerical simulations are conducted for uniform microresonators. The influences of damping, actuation, and fringe effect on the resonator response are found.

On nonlinear response near-half natural frequency of electrostatically actuated microresonators

Different kinds of nanospheres are used in magnetic nanosphere fabrication for bioapplications. In this paper, we report a successful synthesis of magnetic hollow silica nanospheres (MHSNS). The MHSNS were fabricated with a one step coating of Fe3O4 magnetic nanoparticles (NPs)(∼10nm) and silica on nanosized (20–100nm) spherical calcium carbonate (CaCO3) surface under alkaline conditions, in which the nanosized CaCO3 were used as nanotemplates and tetraethoxysilane and magnetic NPs were used as precursors. The as-synthesized nanoshperes were immersed in an acidic solution to remove nanosized CaCO3, forming MHSNS. The MHSNS were characterized by SEM, TEM, and SQUID. SEM and TEM results showed that a smooth surface of MHSNS and a thin layer of silica (∼10nm) embedded with the magnetic NPs was successfully formed. No nanosized CaCO3 nanotemplates were observed. SQUID measurement demonstrated that magnetization of MHSNS was dependent on temperature, exhibiting superparamagnetism. The MHSNS have potential appl...

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Fabrication of magnetic hollow silica nanospheres for bioapplications

Parametric resonance voltage response of electrostatically actuated Micro-Electro-Mechanical Systems cantilever resonators

This paper deals with nonlinear-parametric frequency response of alternating current (AC) near natural frequency electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators. The model includes fringe and Casimir effects, and damping. Method of multiple scales (MMS) and reduced order model (ROM) method are used to investigate the case of weak nonlinearities. It is reported for uniform resonators: (1) an excellent agreement between the two methods for amplitudes less than half of the gap, (2) a significant influence of fringe effect and damping on bifurcation frequencies and phase–frequency response, respectively, (3) an increase of nonzero amplitudes’ frequency range with voltage increase and damping decrease, and (4) a negligible Casimir effect at microscale. [DOI: 10.1115/1.4028887]

Dumitru I. Caruntu

Papers

Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers

On nonlinear response near-half natural frequency of electrostatically actuated microresonators

Fabrication of magnetic hollow silica nanospheres for bioapplications

Parametric resonance voltage response of electrostatically actuated Micro-Electro-Mechanical Systems cantilever resonators

Microelectromechanical Systems Cantilever Resonators Under Soft Alternating Current Voltage of Frequency Near Natural Frequency