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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 deals with the frequency–amplitude response of superharmonic resonance of second order (order two) of electrostatically actuated Micro-Electro-Mechanical System (MEMS) cantilever resonators. The structure of MEMS resonators consists of a cantilever resonator over a parallel ground plate, with a given gap in between, and under AC voltage. This resonance results from hard excitations and AC voltage frequency near one-fourth of the natural frequency of the resonator. The forces acting on the resonator are the nonlinear electrostatic force to include fringe effect, and a linear damping force. In order to solve the dimensionless partial differential equation of motion along with boundary and initial conditions, two types of models are developed, namely Reduced Order Models (ROMs), and Boundary Value Problem (BVP) model. The BVP model is essentially a finite difference model with a discretization in time only. ROMs are developed using one through five modes of vibration. The Method of Multiple Scales (MMS), numerical integrations using MATLAB, as well as a continuation and bifurcation analysis are used to solve the ROMs. The BVP model, resulting from using finite differences for time derivatives, is also numerically integrated. Five modes of vibration ROM is found to make accurate predictions in all amplitudes. A softening effect of the response is predicted. The response consists of a bifurcation with a bifurcation point of amplitude one fourth of the gap, and a stable branch in larger frequencies with a pull-in instability end point at three fourths of the gap. The bifurcation point shifts to lower frequencies as the voltage and/or fringe effect increase, and/or damping decreases. If damping increases, the branches coalesce, peak amplitude decreases, and a linear behavior is experienced.

Frequency–amplitude response of superharmonic resonance of second order of electrostatically actuated MEMS cantilever resonators

Knee Joint Biomechanics for Various Ambulatory Exercises Using Inverse Dynamics in OpenSim

This is a review paper on human knee joint biomechanics modeling. Dynamic models and quasi-static models reported lately in the literature are included in this survey. Anatomical surface representation, contact modeling, ligament structure, and solution algorithm of these models are reviewed.Copyright © 2007 by ASME

Knee Joint Modeling

A new method for systems stability analysis is presented. This method is called weight functions method and it replaces the problem of Liapunov function finding with a problem of finding a number of functions (weight functions) equal to the number of first order differential equations describing the system. It is known that there are not general methods for finding Liapunov functions. The weight functions method is simpler than the classical method since one function at a time has to found. This method’s conditions of solution stability for linear and nonlinear systems are presented. Applications such as Lurie-Postnikov problem and controlled systems stability are presented as well.Copyright © 2005 by ASME

Systems Stability Using Weight Functions Method

This paper deals with a system of two coupled parallel identical MEMS cantilever resonators and a ground plate. Alternating Current (AC) and Direct Current (DC) voltages are applied between the first resonator and ground plate, and a DC voltage applied between the resonators. The AC voltage frequency is near natural frequency of the resonators. The electrostatic forces produced by voltages are nonlinear. System equations of motion are obtained using Lagrange equations, then nondimensionalized. The Method of Multiple Scales (MMS) is used to find the steady state frequency response. The Reduced Order Model (ROM) is used to validate MMS results. Matlab is used to find cantilever frequency response of the resonator tip. The DC voltage between resonators is showed to significantly influence the response of the first resonator.© 2012 ASME

Dumitru I. Caruntu

Papers

Frequency–amplitude response of superharmonic resonance of second order of electrostatically actuated MEMS cantilever resonators

Knee Joint Biomechanics for Various Ambulatory Exercises Using Inverse Dynamics in OpenSim

Knee Joint Modeling

Systems Stability Using Weight Functions Method

Reduced Order Model of Two Coupled MEMS Parallel Cantilever Resonators Under DC and AC Voltage Near Natural Frequency