In recent years, self-balancing personal transportation devices have gained significant popularity, the most popular ones being the “Hoverboard” systems. These systems utilize the dynamics of an inverted pendulum to create stable lateral motion. In this paper, the dynamic behavior of a hoverboard system with an attached flexible beam is investigated. By introducing a flexible beam, the vibrational characteristics of the system created by both the rider and the environment can be measured and accounted for. The beam is a continuous system modeled as an n degree of freedom (DOF) inverted pendulum. The resulting system becomes an n+2 DOF (n DOF for the beam, one DOF for the rotation of the beam about the wheel axis, and one DOF for the horizontal motion of the system). A mathematical model is developed to simulate the vibrations of the beam when excited by a piezoelectric actuator at the base, and to simulate the horizontal motion necessary to balance the beam as it is excited.

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