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.

Analysis of Vibration Control of Nonlinear Beam Using a Time-Delayed PPF Controller

This paper presents a study on the performance of a positive position feedback (PPF) controller to suppress the vibration of a horizontal beam under vertical excitation. Time delays in the control loop are taken into consideration to study their effects on the controller performance and the stable region. The integral iterative method is conducted to obtain a second-order approximate solution and the corresponding amplitude equations for the considered system. The stability of the steady-state solutions is ascertained using a combination of Floquet theory and Hill’s determinant. The maximum limits of time delays at which the system remains stable have been determined for different values of control parameters. And the effects of various control parameters on the existence of multiple-solution region are investigated. The analysis illustrates that the appearance of time delay and the elimination of controller damping coefficient are the two main factors to enhance the nonlinear characteristics of the controlled system. The points at which the steady-state amplitude of the main system reaches its minimum are studied analytically. The analyses show that the analytical results are in excellent agreement with the numerical simulations.

Modeling the Electro-chemical Properties of Microbial Opsin ChrimsonR for Application to Optogenetics-based Vision Restoration

Optogenetic activation of neurons [1] have greatly contributed to our understanding of how neural circuits operate, and holds huge promise in the field of neural prosthetics, particularly in sensory restoration. The discovery of new channelrhodopsins, Chrimson — which is 45 nm more red-shifted than any previously discovered or engineered channelrhodopsin — and its mutant ChrimsonR with faster kinetics [2] made this technology available for medical applications. However, a detailed model that would be able to accurately reproduce the membrane potential dynamics in cells transfected with ChrimsonR under light stimulation is missing. We address this issue by developing the first model for the electrochemical behavior of ChrimsonR that predicts its conductance in response to arbitrary light stimulation. Our model captures ON and OFF dynamics of the protein for stimuli with frequencies up to 100 Hz and their relationship with the brightness, as well as its activation curve, the steady-state amplitude of the response as a function of light intensity. Additionally, we capture a slow adaptation mechanism at a timescale at the order of minutes. Our model holds for light intensities covering the whole dynamic range of the channel (from response onset to saturation) and for timescales in the order of up to several minutes. This model is a new step towards modeling the spiking activity of ChrimsonR-expressing neurons, required for the precise control of information transmission in optogenetics-based Brain-Computer Interfaces, and will inform future applications of ChrimsonR based optogenetics.

Parametrically Excited Electrostatic MEMS Cantilever Beam With Flexible Support

Parametric resonators that show large amplitude of vibration are highly desired for sensing applications. In this paper, a microelectromechanical system (MEMS) parametric resonator with a flexible support that uses electrostatic fringe fields to achieve resonance is introduced. The resonator shows a 50% increase in amplitude and a 50% decrease in threshold voltage compared with a fixed support cantilever model. The use of electrostatic fringe fields eliminates the risk of pull-in and allows for high amplitudes of vibration. We studied the effect of decreasing boundary stiffness on steady-state amplitude and found that below a threshold chaotic behavior can occur, which was verified by the information dimension of 0.59 and Poincaré maps. Hence, to achieve a large amplitude parametric resonator, the boundary stiffness should be decreased but should not go below a threshold when the chaotic response will appear. The resonator described in this paper uses a crab-leg spring attached to a cantilever beam to allow for both translation and rotation at the support. The presented study is useful in the design of mass sensors using parametric resonance (PR) to achieve large amplitude and signal-to-noise ratio.

Unsteady Thermo-Structural Simulation of Nano-Bridge Resonators

This study provides a thermo-structural simulation to investigate the behavior of nano-bridge resonators. A three-dimensional doubly clamped bridge with a length of 10 microns, a width of 1 micron and a thickness of 300 nm vibrating in the air is simulated. A free molecular heat transfer model is used to define the heat transfer coefficient and the damping coefficient. A Finite Difference method is used to solve the transient heat transfer equation coupled with the dynamic structural equation at each time step. The study is performed for silicon. The results show the steady state amplitude variations and vibration amplitude variations by the total heat amplitude correspond to a linear system. The results also show that increasing the total heat amplitude has more significant effects on increasing the vibration amplitude rather than the steady state amplitude by a factor of 1.2. The steady state amplitude and vibration amplitude variation by the surrounding gas pressure is investigated over a range of pressures from 1 kPa to 500 kPa for a total heat amplitude of 5000 MW/m2 (50 mW). The steady state amplitude and the vibration amplitude decrease by increasing the pressure due to an increase in the damping coefficient and the heat transfer coefficient. The rate of decrease is significantly higher for the vibration amplitude. This is due to the combination of increasing heat transfer coefficient, and increased damping, as the pressure increases.

Oblique collisions of internal wave beams and associated resonances

Quadratic nonlinear interactions between two colliding internal gravity wave beams in a uniformly stratified fluid, and the resulting radiation of secondary beams with frequencies equal to the sum and difference of those of the primary beams, are discussed. The analysis centres on oblique collisions, involving beams that propagate in different vertical planes. The propagation directions of generated secondary beams are deduced from kinematic considerations and the use of radiation conditions, thus extending to oblique collisions previously derived selection rules for plane collisions. Using small-amplitude expansions, radiated-beam profiles at steady state are also computed in terms of the characteristics of the colliding beams. It is pointed out that, for certain oblique collision configurations, radiated beams with frequency equal to the difference of the primary frequencies have unbounded steady-state amplitude. This resonance, which has no counterpart for plane collisions, is further analysed via the solution of an initial-value problem; ignoring dissipation, the transient resonant response grows in time like ${t}^{1/ 2} $, a behaviour akin to that of forced waves at cut-off frequencies.

Minimization of the Amplitude of the Entire Span of Beams Using Mass Dampers

The aim of this work is the reduction of the steady state amplitude of harmonically forced simply supported beams using mass dampers. The considered system consists of a mass damper attached to a simply supported beam with a harmonic force applied at a given point along its span. Traditionally, passive vibration devices such as mass spring dampers or mass dampers were attached to beams and carefully designed to minimize the maximum amplitude at a given point along their span. Since minimizing the amplitude at one point of the beam might increase it at another point, in this work the maximum amplitude along the entire beam span is minimized. The problem is solved first using an approximate method. For a given mass ratio, the optimal location of the mass damper is determined first, and then the optimal damping constant is calculated. Fixed-lines of the amplitude of the entire span of the beam which are independent of the damping constant are determined. The optimal placement of the mass damper is chosen such that the maximum of these lines is minimized. Then, the optimal damping constant is obtained analytically from an average of two damping ratios corresponding each to one of the peaks of the amplitude of the entire beam span to coincide with one of the two equally leveled maxima of the fixed-lines. The optimal placement and damping constant are calculated for all possible positions of the point force on the beam. These results are compared to those obtained from an exact numerical optimization procedure. The results are written in dimensionless form and can be applied to a system with any material and geometric properties.

Sensitivity Analysis of a Generic Wake-Body Model for the Vortex-Induced Vibration of a Rigid Circular Cylinder Using Monte Carlo Simulations

A Monte Carlo analysis using pseudo-random sampling is carried out with the objective of determining the relative importance of each of k = 5 independent input parameters appearing in a typical wake-body model for the vortex-induced vibration of an elastically-mounted rigid circular cylinder in uniform flow. For simplicity, the marginal probability distribution of each parameter is assumed to be a uniform distribution. Furthermore, the standard deviation of each distribution is assumed to be the same. The choice of the uniform distribution is also a reflection of the fact that exact forms for the distributions are not known. The sensitivity analysis indicates that the most important factor from the point of view of the predicted steady-state amplitude of oscillation of the cylinder yo is parameter M, which represents the scaling of the effect of the wake on the structure.

Friction-Induced Vibration in Lead Screw Systems: Mathematical Modeling and Experimental Studies

Lead screw mechanisms are used to convert rotary to linear motion. The velocity-dependent coefficient of friction at the contact between lead screw and nut threads can lead to self-excited vibrations, which may result in excessive noise generated by the system. In this paper, based on a practical example of a powered automotive seat adjuster, the nonlinear dynamics of lead screw systems is studied. A test setup is developed to perform experiments on the horizontal motion drive. The experimental results are used in a novel two-step identification approach to estimate friction, damping, and stiffness parameters of the system. The identified parameters together with other known system parameters are used in the numerical simulations. The accuracy of the mathematical model is validated by comparing numerical simulation results with actual measurements in cases where limit cycles are developed. Using simulation results for a range of lead screw angular velocities and axial forces, regions of stability were found. Also, the effects of damping and stiffness parameters on the steady-state amplitude of vibration were investigated.