Dynamics

Research Samples

Student: Prithvi Akella
Professor/Sponsor: Professor Oliver O'Reilly
Mentor: Evan Hemingway
Research Project Title: A Visualization Tool for the Vibration of Euler-Bernoulli and Timoshenko Beams

 

Final Paper

 

Student:  Prithvi Akella
Professor/Sponsor:  Professors Oliver O'Reilly & Kameshwar Poolla
Mentor:  Evan Hemingway
Research Project Title:  Dynamics of Deformed Beams //  Linearization of Neural Networks

 

Abstracts:

 

Deformation of Beams

 

Timoshenko beam deformation is widely considered an upper-division/graduate level topic in the study of beam deformation, while its counterpart, Bernoulli-Euler, is oftentimes taught in lower division undergraduate classes. The aim of our work is to generate Mathematica code to portray both static and vibrational deformation under both prevailing theories. Our intended goal is to create software that assists in the intuition and visualization of deformation under these theories in an effort to facilitate their instruction to an undergraduate audience. To that effect, we hope to publish our work on the Mathematica demonstrations site soon.

 

Linearization of Neural Networks

 

In practice, the functionality of Neural Networks is oftentimes abstracted to a form of linear regression. Our work aims to validate that abstraction by establishing an analytic map between the functionality of each layer in a Net and each successive independent function in a linear regressor. We hope that doing so can not only elucidate why Neural Networks work as well as they do, but also drastically reduce training and estimation times for small data-sizes. If successful, we hope to create linear predictors for stock-market data to validate the functionality of the regressor on highly-variable, real-world data.

 

Student:  Loren Newton
Professor/Sponsor:  Professor Fai Ma
Research Project Title:  Response Approximation of Damped Systems by Damped Mode Fitting

Abstract

 

Student: Tung Phan
Professor/Sponsor: Professor Oliver O'Reilly
Mentor: Alyssa Novelia
Research Project Title: Dynamic Simulation of Rigid Bodies using JavaScript

 

Abstract:
This project involves programming several interactive animations of rigid bodies using JavaScript. The resulting animation modules feature arbitrary rotations of rigid bodies and will be showcased on the instructional website http://rotations.berkeley.edu/. The first module features a simulation of a solid block thrown into empty space and can be used to demonstrate the well-known instability of rotation about the intermediate axis. The interface allows the user to adjust the initial angular and linear velocities as well as the gravitational acceleration. The module can be used to show the evolution of the system's variables with time, and draw the trajectory of the center of mass of the block. The second module involves Euler's representation of a rotation in terms of an axis of rotation and an angle of rotation. The module features two coordinate systems whose rotation can be controlled by the user and a third fixed system that serves as a reference. To use the program, the user needs to input two pairs of axes and angles of rotation for the two controllable sets of axes. Upon the user's command, an animation is shown to help them visualize the results of their inputs and enables them to compare two different rotations.