Showing papers by "Dumitru I. Caruntu published in 2018"

Voltage Response of Circular Plate MEMS Resonators Under Superharmonic Resonance

Abstract: The superharmonic resonance of second order of microelectro-mechanical system (MEMS) circular plate resonator under electrostatic actuation is investigated. The MEMS resonator consists of a clamped circular plate suspended over a parallel ground plate under an applied Alternating Current (AC) voltage. The AC voltage is characterized as hard excitation, i.e. the magnitude is large enough, and the operating frequency is near one-fourth of the natural frequency of the resonator. Reduced Order Model (ROM), based on the Galerkin procedure, transforms the partial differential equation of motion into a system of ordinary differential equations in time using mode shapes of vibration of the circular plate resonator. Three numerical methods are used to predict the voltage-amplitude response of the MEMS plate resonator. First, the Method of Multiple Scales (MMS) is directly applied to the partial differential equation of motion which is this way transformed into zero-order and first-order problems. Second, ROM using two modes of vibration is numerical integrated using MATLAB to predict time responses, and third, the AUTO 07P software for continuation and bifurcation to predict the voltage-amplitude response. The nonlinear behavior (i.e. bifurcation and pull-in instability) of the system is attributed to the inclusion of viscous air damping and electrostatic force in the model. The influences of various parameters (i.e. detuning frequency and damping) are also investigated in this work.

2-D Inverse Dynamics Knee Model: Aligning Anatomical Knee Model With Knee Extension Kinematic Data Using Ligament Forces

Abstract: This paper deals with aligning knee geometrical anatomical data with kinematic data from experimental work in order to develop a two-dimensional inverse dynamics anatomical model of human knee. Motion capture cameras were used to collect the experimental data for a knee extension exercise. Reflective markers were placed on the subjects’ skin during the experiment. In this model, joints such as hip, knee, and ankle are represented by axes of rotation. These axes are determined by calculating the relative instantaneous center of rotation of one body segment with respect to an adjacent body segment. Body-fixed coordinate systems were defined using three reflective markers attached to the subject. The origin of each body fixed-coordinate system was located between the three markers on that body segment, the body-fixed x-axis was pointing towards the marker on the lateral side of the body segment, and the body-fixed y-axis fell on the same plane as the three reflective markers on the body segment. Moreover, the axis of rotation that represents the hip was determined by calculating the instantaneous center of rotation of reflective markers located on the pelvis with respect to a body fixed coordinate system on the thigh. The axis of rotation on the knee was determined by calculating the instantaneous center of rotation of reflective markers on the shin (tibia) with respect to the body-fixed coordinate system on the thigh (femur). The axis of rotation on the ankle was determined by calculating the instantaneous center of rotation of reflective markers on the shin with respect to a body-fixed coordinate system on the foot. Bone anatomical geometries of femur and tibia were represented mathematically as polynomials and superimposed over the experimental data. This was done by matching the center of rotation from experimental data with the geometric center of the femoral condyle. This is necessary for estimating the insertions/origins of knee ligaments. These ligaments are modeled as nonlinear elastic springs. Furthermore, ligaments were divided into separate fiber bundles. Both the posterior and anterior cruciate ligaments were divided into an anterior and posterior fiber bundle. The cruciate ligament forces for both exercises are discussed in this paper.