Presentation Title

Driven FPU Simulation of Structural Correlation in Drone Emission

Faculty Mentor

Enson Chang

Start Date

18-11-2017 2:00 PM

End Date

18-11-2017 2:15 PM

Location

9-263

Session

Physical Sciences 3

Type of Presentation

Oral Talk

Subject Area

physical_mathematical_sciences

Abstract

The objective of our research is to identify an Unmanned Aerial System (UAS) according to the correlation between its structural vibration frequencies. We used an alternative form of the original Fermi Pasta Ulam (FPU) Problem to analyze a one dimensional spring mass system which experienced damping and a weak non-linear force. The original FPU problem has fixed ends and exhibits a highly non-ergodic behavior. In our research, we added a single driving force that emulates the UAS propellers and used a 4th order Runga-Kutta method to model its dynamics. It was thought that the energy put into the system would spread through more of the frequency modes over time. A principal component analysis of the simulation results indicates that energy flowed from the first mode into22 principal components in a 32-mass system over the simulation interval. In contrast, the non-driven FPU system under the same conditions only spreads to 6 – 10 principal components. We conclude that having a single driving force does allow the further distribution of energy throughout the system, making its behavior much more ergodic. The principal components represent correlated modal behaviors which may be exploited to identify the UAS.

Summary of research results to be presented

1. A structural vibration simulation with damping and weak nonlinearity was developed to model the drone structure. The model used 4th order Runga-Kutta method to solve the structural differential equations. 2. We simulated the classic Fermi-Pasta-Ulam (FPU) configuration with fixed boundary conditions. 3. We also simulated the problem with a source driving one end of the system. 4. We applied principal component analysis (PCA) to examine the spread of energy into different degrees of freedom in the system. The classic FPU result was highly non-ergodic, concentrating in the energy in several prinicipal components. This result agrees with past findings. 5. The driven problem showed spreading of energy into many more degrees of freedom. 6. These results showed clear correlation between different vibration modes. These correlations may be a unique signature of a particular drone.

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Nov 18th, 2:00 PM Nov 18th, 2:15 PM

Driven FPU Simulation of Structural Correlation in Drone Emission

9-263

The objective of our research is to identify an Unmanned Aerial System (UAS) according to the correlation between its structural vibration frequencies. We used an alternative form of the original Fermi Pasta Ulam (FPU) Problem to analyze a one dimensional spring mass system which experienced damping and a weak non-linear force. The original FPU problem has fixed ends and exhibits a highly non-ergodic behavior. In our research, we added a single driving force that emulates the UAS propellers and used a 4th order Runga-Kutta method to model its dynamics. It was thought that the energy put into the system would spread through more of the frequency modes over time. A principal component analysis of the simulation results indicates that energy flowed from the first mode into22 principal components in a 32-mass system over the simulation interval. In contrast, the non-driven FPU system under the same conditions only spreads to 6 – 10 principal components. We conclude that having a single driving force does allow the further distribution of energy throughout the system, making its behavior much more ergodic. The principal components represent correlated modal behaviors which may be exploited to identify the UAS.