Harmonic generation and mode conversion in a rigid duct with a time-modulated diaphragm: A computational study

We present a computational study of scattering of linear acoustic waves in a rigid waveguide by an infinitesimally thin vertical rigid baffle whose penetration into the cross-section varies with time. The stationary-baffle case is analysed first to provide a benchmark multimodal description of the scattered field together with the associated reflection and transmission behaviour. We then introduce a periodic modulation of the penetration height, which converts an incident monochromatic wave into a family of temporal harmonics. This interaction is captured through a Floquet-scattering formulation in which the harmonic amplitudes are coupled by interface conditions imposed at the baffle location and solved numerically by truncating the harmonic system. In the long-wavelength regime, we additionally derive a reduced one-dimensional model where the baffle is represented by jump relations that encode the effective kinematic and dynamic constraints induced by partial blockage. For sufficiently slow modulation, a quasistatic approximation is developed and compared against the full Floquet solution. All results are obtained from a self-contained computational framework whose convergence and accuracy are verified throughout. The results demonstrate how time-dependent internal elements redistribute acoustic energy across harmonics and modify reflection and transmission, providing practical modelling tools for waveguides with mechanically driven or actively controlled internal boundaries.