Current Research Projects

Mechanics of Marine Technologies

Many marine technologies have interesting nonlinear dynamics and fluid-structure interaction. The research we conducted in this area includes riser dynamics, oar blade design optimization and the dynamics of an ocean wave energy converter (WEC) whose mass is modulated by the incident waves.

Risers are used to transport crude oil from and water to a well head. They can be several kilometers long and we are interested in examining hockling of these long flexible rod like bodies as they bend and twist under the influence of ocean waves and currents.

The oar blade optimization work seeks to examine the fluid-structure interaction of a blade as it is pushed through the water. The blades that we are examining are made by Croker and Concept2 and are used by rowing crews including the Cal Women's and Men's crews.

The energy harvesting in the WEC takes advantage of resonance phenomena and the modulation is designed to optimize the energy harvesting capabilities of the WEC by helping to overcome an inherent limitation in all resonant energy harvesters. The research features experimental, modeling, analytical and design components and is challenging because of the wide range of open problems in this area.

Collaborators on this research include Hyung-Taek Kim, Chris Daily-Diamond and Victor Le in addition to Professors Carolyn Judge (Naval Academy), Phil Marcus, N. Sri Namachchivaya (University of Illinois at Urbana Champaign), and Ömer Savaş. Former graduate students Bayram Orazov and Xuance Zhou also contributed to this research group's work on the WEC.

Selected works on the WEC include:

Listings of additional papers can be found here

Dynamics of Contacting Rods, Branched Rods, and Entangled Rods

In this research, we use classical and modern theories of deformable rods to examine the behavior of a wide range of natural and manufactured systems featuring elastic rod-like bodies. The applications of our analysis ranges from predictive models for the growth of plant branches, to the stability of tree-like structures, characterizations of the entangled nature of protein molecules and the stability of MEMS devices featuring dry adhesion.

The applications featured in the research have inspired us to examine a wide range of fundamental issues in the theory of deformable rods. These issues include configuration forces and material momentum, notions of material symmetry for elastic rods, development of novel nonlinear stability criteria for tree-like structures composed of elastic rods and for elastic rods which adhere to substrates with the aid of dry adhesion.

Collaborators on this research include former students Patch Kessler, Nur Adila Faruk Senan, Daniel Peters, and Timothy N. Tresierras, along with Professors Carmel Majidi and John A. Williams.

Selected works on the aforementioned topics include:

Fundamental Issues in the Theories of Rods

While rod theories have been in existence since the time of Euler’s elegant work on the elastica in the 18th century, works on formulating more sophisticated rod theories continues to this day. Much of this work is driven by applications and features nonlinear theories. For example, recent works on rods with helical substructures and/or electrostatic effects have been motivated by the flurry of interesting experiments on DNA molecules. Another set of biology-inspired works have arisen from the need to formulate models for growing plant stems and their time varying material properties.

In our research group, the original motivation for our work in this area came from a desire to develop rational models for axially moving media. The work benefitted greatly from the presence of the late Paul M. Naghdi in our department. His papers, with A.E. Green and several of their co-workers, formed the basis for many of our works. The works on axially moving materials then lead to works on adhesion, shock formation, and material momentum (configurational forces). Our most recent work features branched rods and electromagnetic effects on the deformed states of rods.

Collaborators on this research include former students Nur Adila Faruk Senan, Todd Lauderdale, Tom Nordenholz, Daniel Peters, Jeffrey Turcotte, Timothy N. Tresierras, and Peter Varadi.

Selected works on the aformentioned topics include:

Previous Research Projects

Dynamics of the Spine

The biomechanics of the human spine has been a primary research area in recent years. The research has focused on the development of multiscale models for the human spine. These models range from models for the intervertebral joint to rod-based and multibody-based models for the spine. Supplemented by experimental work conducted in collaboration with Professor Jeffrey C. Lotz’s lab at UCSF, these models have been used to show the effects of total disc replacement on the mechanics of a vertebral joint and the stability of the spine in the sagittal plane. We have also developed a range of open-source models for the lumbar spine that are available on the Open-Sim platform. The collaboration with Jeff’s group has since evolved to examining cost-effective, portable methods to quantify orthopaedic biomechanics and physical therapies.

Further details on the research and publication can be found here. Collaborators on this research include the former students Jenni Buckley, Nur Adila Faruk Senan, Melodie Metzger, David Moody and Daniel Peters, and Professor Jeffrey Lotz.

Selected works on this topic include:

Dynamics of Toys

Dating back at least to Coriolis study of Billiards in the 1830s, toys and games have been the source of inspiration in dynamics for centuries. In the past three decades, several interesting toys have appeared. Among them, Euler’s disk, the Dynabee (Powerball), and Hoberman’s sphere. Working with former students Patch Kessler, David Gulick and Peter Varadi on these toys has lead to many surprising insights and conjectures. For Euler’s disk, the conjecture that the abrupt end to its motion is due to vibration driven loss of contact, that the spinup phenomenon in the Dynabee is related to a phenomenon known as resonance capture and features a rolling constraint, and that Hoberman’s sphere provides both a mechanical representation of Gauss’ mutation of space and a realization of Hamilton’s quaternions.

Further details on our work in this area can be found in an article by Mark Frauenfelder in Forefront.

Selected works on this topic include:

Brake Squeal

Brake squeal is a fugitive problem which has occupied researchers for decades. Although widely considered to be a friction-induced vibration phenomenon, the development of accurate models for braking systems and their array of components, and the challenges of analyzing and numerically integrating the resulting equations of motion has meant that this problem continues to feature in the vibrations and vehicle dynamics literature.

Our first research on this topic involved conducting a comprehensive review of work performed on disc brake squeal. This work lead to a publication in 2003 which has since been cited over 300 times and is the most cited work on brake squeal in the literature. Several open problems in the area also became apparent. The first of these was the lack of work on brake squeal induced by the braking event - most research assumed that the brake rotor’s speed was constant. Our resulting analysis with a simple model lead to the conclusions that two-dimensional stick-slip phenomena which naturally arose during a braking event could lead to a broad spectral excitation of the brake rotor. The second open problem was the issue of spectral analyses of linear M-C-K systems where the stiffness matrix was non-symmetric. Such systems feature prominently in models for braking systems. Using a pseudospectral analysis we were able to show how sensitive these models were to spectral instabilities near critical values of the system parameters. These results may eventually lead to an explanation for why brake squeal is so sensitive to the parameters of the braking system.

Collaborators on this research included the former students Patch Kessler, Nathan Kinkaid, and Anne-Lise Raphael, and Professors Panos Papadopoulos and Maciej Zworski.

Selected works on the aformentioned topic include:

The research we conducted on this topic started in 2000 and was funded by a 4 year grant from the NSF and a one-year grant from the Center for Pure and Applied Mathematics at U.C. Berkeley.

Vehicle Dynamics

Our two main former research projects on vehicle dynamics featured a motorcycle and Charles Taylor’s one-wheeled vehicle.

For the motorcycle, the research involved finding a robust algorithm for tracking motorcycles that is suitable for use in real time. Because of the engine-induced vibration in a motorcycle we found that using a set of 3 accelerometers and 3 gyroscopes was not as robust as expected. Instead, the algorithm we proposed and tested using a novel roll angle predictor which used motorcycle speed and a single gyrosope measurement of the angular velocity of the chassis along a vertical axis that corotated with the motorcycle. The experimental results of this research weren’t published, but the algorithm can be found in the paper cited below.

A former student in ME104, Tony Urry, brought Charles Taylor’s one-wheeled vehicle to our attention. A series of these machines was developed and patented by Taylor in the 1950s and 1960s. The goal of the research was to determine how this machine operated. Over the course of five years various models were developed and analyzed and eventually an understanding of how the machine stabilized was developed. Much work remains to be performed analyzing this machine, however the website we developed has lead to renewed interest in Taylor’s work. Hopefully, it will inspire others to reconstruct his prototypes.

Collaborators on this research included the former students Joshua Coaplen, Patch Kessler, Avery Jutkowitz, Eric Lew, Gwo-Jen Lo, Bayram Orazov, Dan Stevens, Peter Varadi, and Professors Karl Hedrick and Panos Papadopoulos.

Published works on this topic include: