Document Type

Honors Thesis


To design and analyze a vibrational plate design, multiple steps must be followed to find the time response of the system. The design was created using an existing patent for the design objectives and the technology that must be avoided. The design was then created using a Delrin plastic sheet, a set of springs, 4 linearization bearings and a vibrational motor. From this point a Free-Body Diagram was set up to find the governing equations of the system. Using these equations, the time response was found using two different numerical methods: the ODE45 program within MATLAB and Laplace/Inverse Laplace. Using ODE45, the displacement of the vibrational sheet was found and using this result, various parameters were adjusted to reach a displacement of 0.1-0.2-inches. These parameters include the number of springs, the spring constant and the size of the eccentric mass. With these parameters in place, the ODE45 time response was found to be 0.25 inches for a user of 188lbs. When the same system is analyzed using the Laplace and Inverse Laplace by hand method, the displacement was found to be 0.26 inches. This represents a 6% difference in the results of the two methods. For this application that only shows a 0.01-inch difference. These two solutions represent effectively equal results.

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