Showing papers by "Dumitru I. Caruntu published in 2019"

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

Abstract: This paper investigates the voltage–amplitude response of superharmonic resonance of second order (order two) of alternating current (AC) electrostatically actuated microelectromechanical system (MEMS) cantilever resonators. The resonators consist of a cantilever parallel to a ground plate and under voltage that produces hard excitations. AC frequency is near one-fourth of the natural frequency of the cantilever. The electrostatic force includes fringe effect. Two kinds of models, namely reduced-order models (ROMs), and boundary value problem (BVP) model, are developed. Methods used to solve these models are (1) method of multiple scales (MMS) for ROM using one mode of vibration, (2) continuation and bifurcation analysis for ROMs with several modes of vibration, (3) numerical integration for ROM with several modes of vibration, and (4) numerical integration for BVP model. The voltage–amplitude response shows a softening effect and three saddle-node bifurcation points. The first two bifurcation points occur at low voltage and amplitudes of 0.2 and 0.56 of the gap. The third bifurcation point occurs at higher voltage, called pull-in voltage, and amplitude of 0.44 of the gap. Pull-in occurs, (1) for voltage larger than the pull-in voltage regardless of the initial amplitude and (2) for voltage values lower than the pull-in voltage and large initial amplitudes. Pull-in does not occur at relatively small voltages and small initial amplitudes. First two bifurcation points vanish as damping increases. All bifurcation points are shifted to lower voltages as fringe increases. Pull-in voltage is not affected by the damping or detuning frequency.

Human Knee Inverse Dynamics Model of Vertical Jump Exercise

Abstract: This work deals with the dynamics of the human knee during vertical jump exercise. The focus is on the joint forces necessary to produce the jump and to dissipate energy during landing. A two-dimensional (2D) sagittal plane, inverse dynamics human leg model is developed. This model uses data from a motion capture system and force plates in order to predict knee and hip joint forces during the vertical jump exercise. The model consists of three bony structures femur, tibia, and patella, ligament structures to include both cruciate and collateral ligaments, and knee joint muscles. The inverse dynamics model is solved using optimization in order to predict joint forces during this exercise. matlab software package is used for the optimization computations. Results are compared with data available in the literature. This work provides insight regarding contact forces and ligaments forces, muscle forces, and knee and hip contact forces in the vertical jump exercise.

Voltage effect on amplitude–frequency response of parametric resonance of electrostatically actuated double-walled carbon nanotube resonators

Abstract: This work deals with the amplitude–frequency response of coaxial parametric resonance of electrostatically actuated double-walled carbon nanotubes (DWCNTs). Nonlinear forces acting on the DWCNT are intertube van der Waals and electrostatic forces. Soft alternating current (AC) excitation and small viscous damping are assumed. In coaxial vibration, the outer and inner carbon nanotubes move synchronously (in-phase). Euler–Bernoulli beam model is used for DWCNTs of high length-to-diameter ratio. Modal coordinates are used for decoupling the linearized differential equations of motion without damping. The reduced-order model (ROM) method is used in this investigation. All ROMs using one through five modes of vibration (terms) are developed in terms of modal coordinates. ROM using one term is solved and frequency–amplitude response predicted by using the method of multiple scales (MMS). All other ROMs using two through five terms are numerically integrated using MATLAB in order to simulate time responses of the structure and also solved using AUTO-07P, a software package of continuation and bifurcation, in order to predict the frequency–amplitude response. All models and methods are in agreement at lower amplitudes, while in higher amplitudes only ROM with five terms provides reliable results. The effects of voltage and damping on the amplitude–frequency response of electrostatically actuated DWCNTs are reported. It is shown that increasing voltage and/or decreasing damping results in a larger range of frequencies for which pull-in occurs.