Title

Parametric Pendulum

Presenter Information

Matthew Laurent

Department

Mechanical and Aerospace Engineering

Major

Mechanical Engineering

Research Advisor

Stutts, Daniel S.

Advisor's Department

Mechanical and Aerospace Engineering

Funding Source

Mechanical and Aerospace Engineering

Abstract

Although parametric resonance occurs in areas disparate as quantum mechanics, cosmology, and the mechanics of machinery, very few students in the physical sciences and engineering are ever exposed to the concept. The presence of time-varying coefficients in the differential equations describing a parametrically excited system leads to a rich set of dynamical behaviors, including counter-intuitive stability or instability. The study presented here describes a simple mechanical system consisting of a pendulum suspended on a pivot driven harmonically up and down by a slider-crank mechanism, and the mathematical model describing the angular position of the pendulum as a function of time. Floquet analysis is used to predict both the presence of stable and unstable parametric combinations of angular velocity and slider-crank length for the up and down pendulum equilibrium pendulum positions. These predictions are verified experimentally using a machine designed and built for this purpose.

Biography

Matthew transferred to Missouri S& Tin Fall of 2010 and will be graduating in May 2013 with a B. S. in Mechanical Engineering. This is his second undergraduate research that he has done. He has also been a very involved member in Missouri S& Ts Formula SAE design team, and held office as Team Leader from June 2011 to June 2012.

Research Category

Engineering

Presentation Type

Poster Presentation

Document Type

Poster

Location

Upper Atrium/Hallway

Presentation Date

03 Apr 2013, 1:00 pm - 3:00 pm

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Apr 3rd, 1:00 PM Apr 3rd, 3:00 PM

Parametric Pendulum

Upper Atrium/Hallway

Although parametric resonance occurs in areas disparate as quantum mechanics, cosmology, and the mechanics of machinery, very few students in the physical sciences and engineering are ever exposed to the concept. The presence of time-varying coefficients in the differential equations describing a parametrically excited system leads to a rich set of dynamical behaviors, including counter-intuitive stability or instability. The study presented here describes a simple mechanical system consisting of a pendulum suspended on a pivot driven harmonically up and down by a slider-crank mechanism, and the mathematical model describing the angular position of the pendulum as a function of time. Floquet analysis is used to predict both the presence of stable and unstable parametric combinations of angular velocity and slider-crank length for the up and down pendulum equilibrium pendulum positions. These predictions are verified experimentally using a machine designed and built for this purpose.