Periodic structures with exponentially varying cross-section areas

Resumo

Periodic structures have been used for many years in different areas such as aerial and terrestrial
vehicles, civil engineering structures and many other products. The term periodic structures come from the
repetitive arrangements of smaller structural units, also known as cells. Among the different phenomena
concerning wave propagation of such systems, the most important is probably the Bragg scattering effect. The
Bragg scattering occurs when the wavelength becomes of comparable size to the structural cells. This results in
frequency ranges where waves cannot propagate, known as bandgaps. In this context, this paper proposes the study
of the formation of bandgaps on a mono-coupled periodic structure consisting of longitudinal wave propagation
in rods. The paper proposes the modeling and analysis of finite periodic structures with exponentially varying
cross-section area. An investigation is conducted on the effects of using symmetric and asymmetric cell matrices.
The structure is modeled using the receptance and dynamic stiffness matrices. The transfer matrix method is used
to determine the properties of the structure from the transmissibility of a single cell. Results show that asymmetric
cells have a wider frequency range when compared to symmetric cells; however, occurring at higher frequencies
ranges.