Oliver O'Reilly - Profile on Academia.edu (original) (raw)

Papers by Oliver O'Reilly

International Journal of Non-Linear Mechanics, 2006

A rotation can be represented by a tensor which in turn can be parameterized by an angle of rotat... more A rotation can be represented by a tensor which in turn can be parameterized by an angle of rotation and an axis of rotation. This paper presents the first systematic study of the class of rotation tensors which possess constant angular velocities. In addition to the expected rotations featuring constant axes of rotation and constant angular rates, the existence of two other types of rotation are shown. For these rotations, the time variation of the angle and axis of rotation are coupled by an integrable dynamical system. Although the temporal behavior of the axis and angle of rotation can be complex, it also demonstrated how the rotations can be considered as motions about the angular velocity vector. One of the methods used to show this result is based on an analogue to the geometry of a circular helix. The presence of the class of rotations in rigid body dynamics and twistless helical deformations of rods is also discussed. ᭧

An Evolution Equation for Plant Growth

ASME 2009 Summer Bioengineering Conference, Parts A and B, 2009

ABSTRACT Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Associat... more ABSTRACT Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Numerous linearizations of mechanical systems feature non-normal operators. This is particularly ... more Numerous linearizations of mechanical systems feature non-normal operators. This is particularly the case in follower force systems, gyroscopic systems and models for squealing brakes. In this paper, it is shown that a pseudospectral analysis can illuminate features of these systems including dissipation-induced destabilization and high eigenvalue sensitivity to parameter variation.

A method for relaxing parameter constraints in rigid body dynamics

International Journal of Non-Linear Mechanics, 2005

ABSTRACT As attractive alternatives to a set of three Euler angles, the rotation of a rigidly def... more ABSTRACT As attractive alternatives to a set of three Euler angles, the rotation of a rigidly deforming body is often represented using four or more parameters. The accompanying parameter constraints introduce generalized constraint forces in the equations of motion which can often negate the benefits of a particular parameterization. In this paper, we discuss situations where the parameter constraints are not imposed. Thus, although the body no longer deforms rigidly, it does deform homogeneously. This allows the theory of a Cosserat point (or, equivalently, the theory of a pseudo-rigid body) to be used to establish equations governing its motion. Earlier work on this topic by O’Reilly and Varadi considered the four Euler parameters and the single Euler parameter constraint. Here, we consider Poincaré's six parameter representation of a rotation tensor, and, complementing earlier work, discuss numerical implementation and representative simulations. One of the contributions of this paper is the development of a viscoelastic Cosserat point, whose equations of motion are free from parameter constraints and singularities, that can be used to approximate the motion of a rigid body.

Modeling MEMS resonators with rod-like components accounting for anisotropy, temperature, and strain dependencies

International Journal of Solids and Structures, 2005

Numerous systems can be described using masses and rods in transverse vibration. Motivated by the... more Numerous systems can be described using masses and rods in transverse vibration. Motivated by the desire to model the effects of axial strain and temperature on systems of this type, we develop a procedure to determine the frequencies of transverse vibration of devices composed of rods and rigid masses as functions of these effects. Our models allow for the rods

The dynamics of Charles Taylor’s remarkable one-wheeled vehicle

Regular and Chaotic Dynamics, 2008

In the 1950s and 1960s, Charles F. Taylor designed and tested various prototype one-wheeled vehic... more In the 1950s and 1960s, Charles F. Taylor designed and tested various prototype one-wheeled vehicles. These machines were stabilized and steered using gyroscopes. In this paper, a simple model of a one-wheeled vehicle is presented and analyzed. This analysis explains the ability of these machines to exhibit stable steady motions.

Physical Review Letters, 2007

A method of measuring the extent to which space curves encircle one another is introduced. The me... more A method of measuring the extent to which space curves encircle one another is introduced. The method provides a family of sets which characterize encircling curves, allowing curve pairs that engage, (and also single curves that self-engage) to be distinguished. The method is applied to the backbone chains of protein molecules.

Multibody System Dynamics, 2010

Pulling Apart a Press-Fitted Joint

Mathematics and Mechanics of Solids, 2002

On azimuthal shear waves in a transversely isotropic viscoelastic mixture: Application to diffuse axonal injury

Mathematics and Mechanics of Solids, 2011

Abstract Motivated by studies on a type of brain injury known as diffuse axonal injury, the dynam... more Abstract Motivated by studies on a type of brain injury known as diffuse axonal injury, the dynamic azimuthal shearing of a mixture of a transversely isotropic viscoelastic material which is surrounded by a softer isotropic viscoelastic material is considered. It is ...

On Transverse and Rotational Symmetries in Elastic Rods

Journal of Elasticity, 2006

The influences of transverse and rotational symmetries on the strain-energy functions of elastic ... more The influences of transverse and rotational symmetries on the strain-energy functions of elastic rods are discussed. Complete function bases are presented and, for some constrained theories, these bases are also proven to be irreducible. The treatment of symmetry is based on a reformulation of a recent work by Luo and O’Reilly. It is also shown how this work relates to existing treatments by Antman and Healey for a particular constrained rod theory.

Journal of Applied Mechanics, 2001

On Some Peculiar Aspects of Axial Motions of Closed Loops of String in the Presence of a Singular Supply of Momentum

Journal of Applied Mechanics, 2004

ABSTRACT We consider the dynamics of a closed loop of inextensible string which is undergoing an ... more ABSTRACT We consider the dynamics of a closed loop of inextensible string which is undergoing an axial motion. At each instant, one material point of the string is in contact with a singular supply of linear momentum (also known as an external constraint). Several peculiar features of this problem which have not been previously discussed are presented. These include the possible presence of an arbitrary number of kinks, the vanishing nature of the singular supply of momentum, and the critical nature of the tension in the string. When the linear momentum is supplied by a mass-spring-dashpot system, we are also able to establish an exact expression for the frequency of the resulting vibrations, prove that dissipation cannot be present, show that these vibrations only occur for discrete speeds of axial motion, and establish that Coulomb friction is absent.

International Journal of Engineering Science, 2004

Appropriate balance equations are formulated for a body whose geometry, mass and inertia vary due... more Appropriate balance equations are formulated for a body whose geometry, mass and inertia vary due to surface growth. The distance between any two particles of the body is assumed to be fixed and hence several interesting simplifications of the balance laws occur. In particular, a set of ordinary differential equations for the attitude and position of the body are developed. The dynamics predicted by these equations for a body moving on an incline, and gathering mass as it does so, are discussed.

On the static equilibria of branched elastic rods

International Journal of Engineering Science, 2011

Structures featuring rod-like bodies connected in a branched ensemble are ubiquitous. They appear... more Structures featuring rod-like bodies connected in a branched ensemble are ubiquitous. They appear in antennae, replicating DNA strands, and, most visibly, in the plant kingdom. In spite of this, modeling these branched structures using rod theories have received little attention in the literature. With the help of a general rod theory, which was originally developed by Green and Naghdi, balance laws for these structures are discussed. The governing equations established are then shown to be equivalent to variational principles for tree-like structures. These principles are adopted from works by Ivanov and Tuzhilin and may lead to the development of nonlinear stability criteria for these structures. It is also shown how the conditions at a branching point in these structures can be understood using recent interpretations of Eshelby’s work on material (configurational) forces in adhesion problems. The static configurations are illuminated for several structures using Euler’s theory of the elastica. Instances of multiple possible configurations and novel extensions to the classical problem of the tallest column are also discussed.

European Journal of Mechanics - A/Solids, 2007

Wire ropes, DNA strands and helical springs are among those bodies which can be modeled as an ela... more Wire ropes, DNA strands and helical springs are among those bodies which can be modeled as an elastic rod with a helical substructure. The resulting form of the strain-energy function is a matter of material symmetry. This symmetry is explored using a novel treatment which combines non-affine transformations and a relabeling of the material coordinates. The restrictions this treatment imposes on the strain-energy function include a periodic dependency on torsional strain. In addition, comparisons are made with results from a recent treatment of helical symmetry by Healey. Finally, conclusions applicable to material symmetry restrictions for other polar elastic continua are presented. (O.M. O'Reilly). 1 Healey's work can be viewed as an extension to earlier treatments which were framed in the context of a so-called worm-like chain (WLC) model for double-stranded DNA (

Biomechanics and Modeling in Mechanobiology, 2012

A new musculoskeletal model for the lumbar spine is described in this paper. This model features ... more A new musculoskeletal model for the lumbar spine is described in this paper. This model features a rigid pelvis and sacrum, the five lumbar vertebrae, and a rigid torso consisting of a lumped thoracic spine and ribcage. The motion of the individual lumbar vertebrae was defined as a fraction of the net lumbar movement about the three rotational degrees of freedom: flexion-extension lateral bending, and axial rotation. Additionally, the eight main muscle groups of the lumbar spine were incorporated using 238 muscle fascicles with prescriptions for the parameters in the Hill-type muscle models obtained with the help of an extensive literature survey. The features of the model include the abilities to predict joint reactions, muscle forces, and muscle activation patterns. To illustrate the capabilities of the model and validate its physiological similarity, the model's predictions for the moment arms of the muscles are shown for a range of flexion-extension motions of the lower back. The model uses the OpenSim platform and is freely available on https://www.simtk.org/home/lumbarspine to other spinal researchers interested in analyzing the kinematics of the spine. The model can also be integrated with existing OpenSim models to build more comprehensive models of the human body.

On the evolution of intrinsic curvature in rod-based models of growth in long slender plant stems

ABSTRACT In many applications of rod theories as models for plant stem growth and development, it... more ABSTRACT In many applications of rod theories as models for plant stem growth and development, it is necessary to allow the intrinsic curvature and flexural stiffness of the rod to evolve. In the present paper, the application of evolution equations for these quantities is examined and a new evolution equation for the intrinsic curvature is proposed. To illustrate the new evolution equation, several examples of the evolution of rods in the presence of external forces and tip growth are presented. Growth in plants frequently results in residual stresses and the compatibility of rod models with these fields is also discussed.

On energetics and conservations for strings in the presence of singular sources of momentum and energy

Acta Mechanica, 2003

Summary. This paper discusses the dynamics of strings which are subject to the presence of singul... more Summary. This paper discusses the dynamics of strings which are subject to the presence of singular sources of momentum and energy. Such sources arise naturally in many problems featuring axially moving strings and have been the subject of several recent works. The contribution of the present paper is to present new results pertaining to the time rate of change of

Elastic equilibria of translating cables

Acta Mechanica, 1995

Summary The equations of motion describing the non-linear behavior of a perfectly flexible travel... more Summary The equations of motion describing the non-linear behavior of a perfectly flexible travelling cable are derived from first principles. Influences due to changes in the cross-sectional area of the cable and mass conservation are included. A homogenous isotropic non-linearly elastic cable material is assumed and the qualitative nature of a class of its equilibria is analyzed. The dependence of