Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
The 1:1 Internally Resonant Response Of A Cantilever Beam Attached To A Rotating Body, Christopher Lee, K Murphy
The 1:1 Internally Resonant Response Of A Cantilever Beam Attached To A Rotating Body, Christopher Lee, K Murphy
Christopher Lee
Modal coupling in the dynamics of a cantilever beam attached to a rotating body is investigated using a coupled, non-linear three-degree-of-freedom model which includes the effects of centrifugal stiffening. The near-resonant response of two lateral modes (one in-plane and one out-of-plane as defined by the plane of rotation) driven by a peridoic out-of-plane excitation is examined for the case in which the natural frequencies of the lateral modes are commensurate in a near one-to-one ratio. The existence and stability of periodic solutions are examined using a second order perturbation analysis. Regions in the system parameter space are identified where single- …
Three-Dimensional Oscillations Of Suspended Cables Involving Simultaneous Internal Resonances, Christopher Lee, Noel Perkins
Three-Dimensional Oscillations Of Suspended Cables Involving Simultaneous Internal Resonances, Christopher Lee, Noel Perkins
Christopher Lee
The near resonant response of suspended, elastic cables driven by planar excitation is investigated using a three degree-of-freedom model. The model captures the interaction of a symmetric in-plane mode with two out-of-plane modes. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. For particular magnitudes of equilibrium curvature, the natural frequency of the in-plane mode is simultaneously commensurable with the natural frequencies of the two out-of-plane modes in 1:1 and 2:1 ratios. A second nonlinear order perturbation analysis is used to determine the existence and stability of four classes of periodic solutions. The perturbation solutions …
Model-Based Processing Of Microcantilever Sensor Arrays, Christopher Lee, D Clague, J Tringe, J Candy, A Sinensky, R Rudd, A Burnham
Model-Based Processing Of Microcantilever Sensor Arrays, Christopher Lee, D Clague, J Tringe, J Candy, A Sinensky, R Rudd, A Burnham
Christopher Lee
In this paper, we have developed a model-based processor (MBP) for a microcantilever-array sensor to detect target species in solution. We perform a proof-of-concept experiment, fit model parameters to the measured data and use them to develop a Gauss-Markov simulation. We then investigate two cases of interest, averaged deflection data and multichannel data. For this evaluation we extract model parameters via a model-based estimation, perform a Gauss-Markov simulation, design the optimal MBP and apply it to measured experimental data. The performance of the MBP in the multichannel case is evaluated by comparison to a "smoother" (averager) typically used for microcantilever …
Non-Linear Dynamic Intertwining Of Rods With Self-Contact, Christopher Lee, Sachin Goyal, Noel Perkins
Non-Linear Dynamic Intertwining Of Rods With Self-Contact, Christopher Lee, Sachin Goyal, Noel Perkins
Christopher Lee
Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or ‘hockles’ are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computationalrod model that explicitly accounts for dynamicself-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamicevolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this …