Computational design of flexible structures for vibro-acoustic noise control: A semi-analytical approach

This paper presents a semi-analytical computational framework for the design and analysis of flexible structures for vibro-acoustic noise control. The study focuses on an axisymmetric configuration consisting of a flexible cylindrical shell with elastic membrane discs located at the interfaces. The structure is excited by axial structure-borne waves traveling along the shell, which couple to a membrane-bounded internal cavity and radiate into an extended outlet region. The governing boundary-value problem comprises the Helmholtz equation in the fluid domain and the Donnell–Mushtari shell equations at the radial boundary, leading to eigenfunctions that are non-orthogonal and linearly dependent. At the interfaces, the membrane discs are modeled via a Galerkin projection onto orthogonal membrane modes. Continuity of normal velocity at the interfaces is imposed to couple the orthogonal membrane modes with the non-orthogonal shell–acoustic modes, yielding a linear algebraic system for the symmetric and antisymmetric modal amplitudes. The convergence of the truncated solution is assessed through reconstruction of the continuity conditions and verification of an intrinsic power-conservation identity. Numerical experiments illustrate how system parameters, such as membrane tension and shell radius, influence the filtering and excitation of higher-order fluid–structure coupled modes.