posted on 2018-06-13, 02:43authored byRenan dos Reis, Pedro Hiroshi Ely Ito, Solano Elias Souza Felicio, Fernando Fernandes Paiva
Abstract We propose a device for classroom demonstrations of resonance in cylindrical beams. It comprises a set of beams of different lenghts attached to a ring linked to a vibration source. By adjusting the vibration frequency, one makes beams resonate, allowing qualitative analysis of the vibrational modes. We give a simplified model for the resonance modes, linking each beam's geometry and material to its resonance frequencies. We show that a mode's frequency is inversely proportional to beam length squared, and that given a mode's frequency, geometry and density of a beam, we may calculate its material's modulus of elasticity. We validate our model by experimental results and propose new applications to the device.