Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Predicting attenuation characteristics on finite periodic pinned supported beam structures
Submission Author:
Jean Paulo Carneiro Junior , MS , Brazil
Co-Authors:
Jean Paulo Carneiro Junior, Vinicius Germanos Cleante, Paulo José Paupitz Gonçalves, Michael Brennan
Presenter: Jean Paulo Carneiro Junior
doi://10.26678/ABCM.COBEM2021.COB2021-2338
Abstract
One-dimensional waveguides are frequently found in structural engineering applications. They consist of long and thin elements, such that their properties can be well defined along with a single coordinate system. Examples of such systems include rods, beams, shafts and pipes. Often, these systems are assembled in periodic arrangements, where the whole system consists of a repetition of smaller units, known as cells. The periodicity can occur due to changes in the cell geometry, material properties, attachments, or boundary conditions. In this paper, wave propagation behaviour is investigated for the cases of simply supported beams, which can be modelled as a mono-coupled periodic system. Changes in the geometric properties are also induced to improve the so-called attenuation bands, which are frequency ranges where waves are not cancelled, but severely reduced. Because bending waves are dispersive and dependent on the cross-section shape, the geometric changes are made so that the ratio of the second moment of area and cross-section area between two different beams remain fixed. The analysis consists of modelling a single cell using the concept of displacement transmissibility, which is a measurable quantity. Approximate analytical expressions are derived to predict the bandwidths of the attenuation bands and the maximum attenuation for a single cell. These expressions can be used to estimate the attenuation for a system consisting of N periodic cells.
Keywords
angular transmissibility, periodic structures, Transfer Matrix Method, Pinned stepped beam
