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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

The objective of this study is to determine the three dimensional kinematics of the human pelvis including both sacroiliac joints following a simulated open book fracture induced on cadavers by applying anterior-posterior compressive loads to the pelvis. An electromagnetic digitizing and motion tracking system was utilized to measure the morphology of the pelvis and the relative movements of its bones during this simulated open book fracture. The screw displacement axis method was used to describe the relative motions between the sacrum and each hip bone. Morphologically, it was found that the articular surfaces forming the sacroiliac joints can be approximated with planar surfaces directed from proximal and lateral to distal and medial and from posteromedial to anterolateral. The kinematic data indicate that the motion of the hip bone with respect to the sacrum on the side of the sacroiliac joint (SIJ) opening is almost a pure rotation which translates clinically on the A-P x-rays as pure opening of the SIJ without vertical displacement. The average axis of rotation was found to be almost parallel to the SIJ planar articular surface.Copyright © 2002 by ASME

Kinematics of the Human Pelvis Following Open Book Injury

\n Forcespinning is a novel method that makes use of centrifugal forces to produce nanofibers rapidly and at high yields. To improve and enhance the forcespinning production method, a 2D computational forcespinning inviscid fluid dynamics model is developed. Two models, namely, time-independent and time-dependent, are obtained in order to investigate the effects of various parameters on fiber forcespinning formation (trajectory, jet diameter, tangential velocity). The fluid dynamics equations are solved using the method of multiple scales along with the finite difference method and including slender-jet theory assumptions. It is important to produce jets with small diameters in the micro- and nanorange. Both the Weber (We) and Rossby (Rb) numbers were found to expand the jet trajectory as they increased. Increasing We and/or decreasing Rb was found to decrease the jet diameter. Also, by varying forcespinning parameters, it has been found that the jet radius can be decreased by increasing the jet exit angle in the direction of rotation, reducing the spinneret fluid level, increasing the angular velocity of the spinneret, reducing spinneret length, and/or reducing the orifice diameter. Knowing that jet trajectories are important for designing and positioning of the fiber collector, it has been found that the trajectories expand out with the increase in the jet exit angle in the direction of rotation, increase in the fluid level, increase in the angular velocity, and/or increase in the spinneret length. Production rates and jet radii for any predetermined radial collector distance were also determined.

Two-Dimensional Modeling of Nonlinear Dynamics of Forcespinning Jet Formation

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.

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

Simultaneous resonances, superharmonic and subharmonic, of two-term excitation nonlinear bending vibrations in the case of moderately large curvature of nonuniform cantilever beams are reported. Cantilevers of constant width and parabolic thickness variation are considered in this research. The method of multiple scales is directly applied to the governing partial-differential equation of motion and boundary conditions. Two problems, zero- and first-order, result. Using factorization method, the linear modes of the zero-order problem are obtained in terms of hypergeometric functions. The first-order problem provides the amplitude-phase evolution relationship and consequently the simultaneous resonances response.Copyright © 2009 by ASME

Simultaneous Resonances of Geometric Nonlinear Nonuniform Beams

This paper deals with the effect of Casimir force on the amplitudefrequency response of parametric resonance of electrostatically actuated nanoresonators. The resonator is actuated by using an electrostatic force to include a first order fringe correction. Casimir force and viscous damping force are included in the model, as well. Both electrostatic and Casimir forces are nonlinear. The behavior of the resonator is investigated using two methods, the Method of Multiple Scales (MMS) for a Reduced Order Model (ROM) using one mode of vibration, and numerical integration of ROMs using up to five modes of vibration. ROM is based on the application of a Galerkin procedure that uses the undamped mode shapes of the cantilevered beam as the basis of functions. The amplitude-frequency response consists of two bifurcations, namely subcritical and supercritical. The increase of Casimir effect shows an increase of the interval of frequencies of the unstable zero steady-state solutions, and a larger range of frequencies for which the system has stable steady-state solutions for amplitudes larger than 0.5 of the gap.

Dumitru I. Caruntu

Papers

Kinematics of the Human Pelvis Following Open Book Injury

Two-Dimensional Modeling of Nonlinear Dynamics of Forcespinning Jet Formation

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

Simultaneous Resonances of Geometric Nonlinear Nonuniform Beams

Casimir Effect on Amplitude-Frequency Response of Parametric Resonance of Electrostatically Actuated NEMS Cantilever Resonators