Christopher L. Lee

Non-linear Dynamic Intertwining of Rods With Self-Contact

Abstract 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 computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution 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 helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively, by the dynamic conversion of twist (Tw) to writhe (Wr).

Harvesting vibration energy using nonlinear oscillations of an electromagnetic inductor

Harvesting energy from ambient vibration is a promising method for providing a continuous source of power for wireless sensor nodes. However, traditional energy harvesters are often derived from resonant linear oscillators which are capable of providing sufficient output power only if the dominant frequency of input vibrations closely matches the device resonant frequency. The limited scope of such devices has sparked an interest in the use of nonlinear oscillators as mechanisms for broadband energy harvesting. In this study, we investigate the harvesting performance of an electromagnetic harvester sustaining oscillations through the phenomena of magnetic levitation. The nonlinear behavior of the device is effectively modeled by Duffings equation, and direct numerical integration confirms the broadband frequency response of the nonlinear harvester. The nonlinear harvesters power generation capabilities are directly compared to a linear electromagnetic harvester with similar dynamic parameters. Experimental testing shows that the presence of both high and low amplitude solutions for the nonlinear energy harvester results in a tendency for the oscillator to remain in a low energy state for non-harmonic vibration inputs, unless continuous energy impulses are provided. We conclude by considering future applications and improvements for such nonlinear devices.

Torsional Buckling and Writhing Dynamics of Elastic Cables and DNA

Marine cables under low tension and torsion on the sea floor can undergo a dynamic buckling process during which torsional strain energy is converted to bending strain energy. The resulting threedimensional cable geometries can be highly contorted and include loops and tangles. Similar geometries are known to exist for supercoiled DNA (deoxyribonucleic acid) and these also arise from the conversion of torsional strain energy to bending strain energy or, kinematically, a conversion of twist to writhe. A dynamic form of Kirchhoff rod theory is presented herein that captures these nonlinear dynamic processes. The resulting theory is discretized using the generalized-α method for finite differencing in both space and time. The important kinematics of cross-section rotation are described using an incremental rotation “vector” as opposed to traditional Euler angles or Euler parameters. Numerical solutions are presented for an example system of a cable subjected to increasing twist at one end. The solutions show the dynamic evolution of the cable from an initially straight element, through a buckled element in the approximate form of a helix, and through the dynamic collapse of this helix through a looped form.Copyright

Enhanced vibration energy harvesting using nonlinear oscillations

Results for the design and testing of an electromagnetic device that converts ambient mechanical vibration into electricity are presented. The design of the device is based on an L-shaped beam structure which is tuned so that the first two natural frequencies have a near two-to-one ratio which is referred to as an internal resonance or autoparametic condition. It is shown that in contrast to single degree-of-freedom, linear-dynamics-based vibration harvesters which convert energy in a very narrow frequency band the prototype can generate power over an extended frequency range when subject to harmonic, base displacement excitation.

An Autoparametric, Electromagnetic Ambient Vibration Energy Harvester

Results are presented for the design and testing of an electromagnetic device to convert ambient mechanical vibration into electricity. The design of the device is based on an Lshaped beam structure which is tuned so that the first two (bending) natural frequencies have a (near) two-to-one ratio. This creates an internal resonance or autoparmetic condition that can result in a nonlinear dynamic response to a sinusoidal (base) displacement excitation over an extended frequency range. This is in contrast to single degree-of-freedom, linear-dynamics based vibration harvesters which convert energy in a very narrow frequency band. Representative measurements of displacement and power generated are presented. The problem of fatigue failure in the devices presents limits to their long-term operation.

Correlations Between Quantitative MR Imaging Properties and Viscoelastic Material Properties of Agarose Gel

This study determines and assesses correlations between quantitative magnetic resonance imaging (qMRI) parameters (proton density, diffusion, T1 and T2 relaxation) and viscoelastic material properties (storage modulus) for various low concentrations (0.5–3.0 % weight/volume) of agarose gel. MR imaging was done using a 3T (Philips Achieva) scanner. Dynamic mechanical analysis (DMA) was used to characterize the viscoelastic properties of the gels. The repeatability and accuracy of the DMA measurements have some dependence on various geometric sample and measurement parameters. An optimal set of parameters (for compression mode testing) that would produce reliable and repeatable measurements was identified for ranges of sample geometry. Higher concentrations of agarose were associated with higher storage moduli and lower relaxation times, diffusion coefficients, and proton densities. Of the qMRI parameters, T2 relaxation is the most sensitive to changes in concentration.

Constructing 3D-Printable CAD Models of Prostates from MR Images

This paper describes the development of a procedure to generate patient-specific, three-dimensional (3D) solid models of prostates (and related anatomy) from magnetic resonance (MR) images. The 3D models are rendered in STL file format which can be physically printed or visualized on a holographic display system. An example is presented in which a 3D model is printed following this procedure.

A 3D-Printed Patient-Specific Phantom for External Beam Radiation Therapy of Prostate Cancer

This paper presents the design evolution, fabrication, and testing of a novel patient and organ-specific, 3D printed phantom for external beam radiation therapy of prostate cancer. In contrast to those found in current practice, this phantom can be used to plan and validate treatment tailored to an individual patient. It contains a model of the prostate gland with a dominant intraprostatic lesion, seminal vesicles, urethra, ejaculatory duct, neurovascular bundles, rectal wall, and penile bulb generated from a series of combined T2-weighted/dynamic contrast-enhanced magnetic resonance images. The iterative process for designing the phantom based on user interaction and evaluation is described. Using the CyberKnife System at Boston Medical Center a treatment plan was successfully created and delivered. Dosage delivery results were validated through gamma index calculations based on radiochromic film measurements which yielded a 99.8% passing rate. This phantom is a demonstration of a methodology for incorporating high-contrast magnetic resonance imaging into computed-tomography-based radiotherapy treatment planning; moreover, it can be used to perform quality assurance.

Demonstrations of bio-inspired perching landing gear for UAVs

Results are presented which demonstrate the feasibility and performance of two concepts of biologically-inspired landing-gear systems that enable bird-sized, unmanned aerial vehicles (UAV’s) to land, perch, and take-off from branchlike structures and/or ledges. The first concept follows the anatomy of birds that can grasp ahold of a branch and perch as tendons in their legs are tensioned. This design involves a gravity-activated, cable-driven, underactuated, graspingfoot mechanism. As the UAV lands, its weight collapses a four-bar linkage pulling a cable which curls two opposing, multi-segmented feet to grasp the landing target. Each foot is a single, compliant mechanism fabricated by simultaneouly 3D-printing a flexible thermo-plastic and a stiffer ABS plastic. The design is optimized to grasp structures over a range of shapes and sizes. Quasi-static and flight tests of this landing gear affixed to RC rotorcraft (24 cm to 550 cm in diameter) demonstrate that the aircraft can land, perch, and take-off from a tree branch, rectangular wood board, PVC pipe, metal hand rail, chair armrest, and in addition, a stone wall ledge. Stability tests show that perching is maintained under base and wind disturbances. The second design concept, inspired by roosting bats, is a two-material, 3D-printed hooking mechanism that enables the UAV to stably suspend itself from a wire or small-diameter branch. The design balances structural stiffness for support and flexibility for the perching process. A flight-test demonstrates the attaching and dis-engaging of a small, RC quadcopter from a suspended line.

Determination of the shear moduli of agarose gel using novel optical measurements

The objective of this study was to measure viscoelastic shear (storage and loss) moduli of low concentrations of agarose gel using hyper-frequency viscoelastic spectroscopy which is a non-contacting optical method. Using a Rheospectris C500, measurements were made in an excitation frequency range of 10-1000 Hz. It was found that the magnitudes of the moduli increased with frequency. Favorable comparisons were found to values determined using dynamic mechanical analysis.