Computational time-dependent acoustic scattering in a rectangular membrane–porous waveguide

A semi-analytical, computational framework is developed for the time-dependent propagation, scattering and dissipative decay of a broadband acoustic pulse in a two-dimensional rectangular waveguide whose central segment carries a porous material core bracketed by two clamped flexible membrane strips. The transient treatment follows the wavepacket–Fourier approach. About the centre line the field splits into symmetric and anti-symmetric subproblems; the duct and porous segments are expanded on rigid-wall cosine modes and each membrane on a clamped sine Galerkin basis, whose projection yields a closed-form coupling matrix. The block linear system is validated by point-wise reconstruction of pressure and velocity continuity at every matching plane, by a truncation convergence study, and by two independent energy checks: the absorbed power fraction is recomputed from a dissipation audit of the power fluxes entering and leaving the porous core, and the lossless limit of the porous model is shown to return the incident power in full. The time-dependent field is recovered as a single Gaussian-weighted matrix product over a precomputed wavenumber grid, so that each snapshot costs one matrix–vector product. Numerical experiments delineate transmission, mixed and reflection regimes, locate the membrane–cavity hybrid resonances of maximum absorption, and visualise the transfer of pulse energy to the membranes and porous filler during transit.