Abstract Summary
One of the objectives in the study of periodic structures is the development of passive control techniques dedicated to application in light structures, to reduce the transmission of noise and vibration. Periodic structures have been gaining notoriety in the scientific community for their unique dynamic properties, such as the Bragg scattering effect. The Bragg phenomenon results in ranges of frequencies where waves do not propagate, known as bandgaps. Due to this phenomenon, the study of such structures has excelled in reducing vibration within the desired frequency range. In this context, this work deals with the study of the dynamic behavior of periodic structures composed of rods with non-uniform cross-section areas, in search of the formation of bandgaps in finite mono-coupled structures about the propagation of longitudinal waves. The work proposes the modeling and analysis of finite periodic structures with exponentially varying cross-section areas, with conically varying cross-section areas, and with catenoid varying cross-section areas. Structures are modeled using dynamic stiffness and receptance matrices. The transfer matrix method is used to determine the properties of the entire structure from the structural properties of a single cell. Analytical expressions representing the transmissibility of structures composed of a single cell are also calculated. An analysis regarding the geometry of the structure is performed on the use of asymmetric and asymmetric cells. The importance of the orientation of asymmetric cells in relation to the excitation force is highlighted. To validate the methodology, experimental tests were carried out with a structure composed of rods with conically varying cross-section areas. The results show that in relation to bandwidth and minimum transmissibility, structures composed of rods with exponentially varying cross-section areas, with conically varying cross-section areas and with catenoid cross-section areas present similar responses. In relation to cell orientation, asymmetrical cells present better performance than symmetrical cells, however, the frequency band occurs in a higher frequency range.
