A Model Of Linear And Nonlinear Behavior Of Coupled Wave Systems On A Wilberforce Pendulum Lattice

CPT Mark R Haseman, USA

We develop a model system called the Wilberforce pendulum lattice to analytically and numerically investigate the physics of coupled wave systems. Linear and nonlinear behavior is explored. The lattice consists of a one-dimensional lattice of pendulums in a uniform gravitational field. The pendulums are pivoted on a single axis, and are connected to each other by springs that are concentric to the axis. The pendulums are free to oscillate angularly transverse to the axis and longitudinally along the axis, so the system supports both transverse and longitudinal waves. Furthermore, these motions are linearly coupled due to the tendency of springs to coil and uncoil during compression and extension. The linear normal modes exhibit the phenomenon of mode level repulsion. There are many cases in nature where this behavior is observed, such as neutrino oscillations, sound in liquid-filled nonrigid pipes, and sound in porous media on the ocean floor. We use the lattice to visualize coupled waves in a closed system for standing waves, as well as an open system for traveling extended waves and wave packets. For nonlinear motion of the lattice, we investigate new types of solitary waves, which are localized nonlinear waves of permanent shape.

Point of Contact:

rharkins@nps.edu

Added:

Jul 10, 2014

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