Analytical-numerical study of natural frequencies and mode shapes of interconnected acoustic cavities due to the influence of several significant parameters

Resumo

Nuclear power plants, industrial plants, refineries, and other engineering installations, are made up of
tubular circuits traversed by fluids, and the dynamic response of these systems excited by flows, are characterized

by fluid-structure problems of great interest in engineering projects. This paper presents a comparative analytical-
numerical study on the behavior of interconnected acoustic cavities, considering the influence of several significant

parameters, such as the number of tubes, the boundary conditions and section changes of the circuit. As a response
to the analysis, natural frequencies and mode shapes are obtained by comparing an analytical method and
numerical modeling. The analytical formulation was developed from the classic idea of the Transfer Matrix

Method (TMM), considering different boundary conditions at the ends of the circuit, such as the open-open, closed-
closed and closed-open system. For all cases, the fundamental equation composed by the association of several

interconnected elements is obtained. All analyzes were compared with numerical simulations obtained by the
Finite Element Method (FEM), with the aid of the commercial software ANSYS. The cases treated in this paper
include the evaluation of the effects of these parameters, oriented to applications in tubular circuits, present in
industrial plants, analyzing the behavior of the acoustic pressures and flows in these cavities, through the study of
natural frequencies and mode shapes in each case. There is a good agreement of the results obtained by the Finite
Element Method in comparison with the analytical solutions obtained by the Transfer Matrix Method. Thus, the
study of the behavior of acoustic cavities interconnected by different methods, in addition to enabling the validation
of this simple analytical formulation, allows the preliminary treatment of the problem, for the fluid-structure
approach, which is a more complex issue and dependent on these analyzes.