• Analytical model for computing acoustic flow in a fan intake • Suitable for flutter bite and noise studies at low and high frequencies • Supports arbitrary number of acoustic treatments in the model • Well-conditioned formulation enables use of direct solvers • Application to the contribution of liners to fan flutter Acoustic treatments are used in modern aeroengines to reduce community noise. Recent studies have highlighted an acoustic-driven instability known as flutter bite. This phenomenon arises at frequencies lower than those associated with noise, where an upstream acoustic wave, generated by fan vibration, is reflected at the duct inlet, forming a feedback loop. To study acoustic behavior over a wide frequency range, we introduce a new model. It consists of an annular duct with an arbitrary number of sections, each potentially featuring different acoustic treatments. The acoustic wave propagation inside the intake is solved analytically, and a mode-matching technique is employed to handle transitions between sections. Unlike previous approaches, we formulate the problem to obtain a numerically well-conditioned linear system, enabling the use of direct solvers instead of iterative ones. We discuss the convergence with respect to the number of radial modes and improve it through an appropriate choice of projection functions, even for low impedance values. Two illustrative applications are presented: the analysis of flutter bite in a fan intake with a single liner, and a study of the effect of multiple acoustic treatments.

• General SOV-type plate to elastically restrained boundaries. • Closed-form DSM for orthotropic rectangular plates. • W–W algorithm avoids direct eigenvalue solving. • Explicit closed-form J0 term for the W–W algorithm. • Mode shapes computed for arbitrary boundary conditions. A separation-of-variable dynamic stiffness method (SOV-DSM) is proposed for the free vibration analysis of an thin orthotropic rectangular plate with general homogeneous boundary conditions. Firstly, the extended SOV solution satisfying Rayleigh’s principle is extended to handle arbitrary boundary conditions and then applied to develop closed-form dynamic stiffness formulations. Then, an enhanced Wittrick–Williams (W-W) algorithm is used to solve the eigenvalue problem rather than solving the highly nonlinear eigenvalue equations. The J 0 count problem involved in applying the W-W algorithm is addressed by providing an explicit and closed-form expression for the J 0 term based on the characteristics of the SOV solution. Furthermore, a numerical technique is provided to calculate the mode shape of the plate with any arbitrary boundary conditions. The accuracy of the proposed method is validated through numerical experiments by comparison with other analytical solutions.