In this work, we present a comprehensive experimental study on the problem of harmonic oscillations of rigid plates with H-shaped cross sections submerged in a quiescent, Newtonian, incompressible, viscous fluid environment. Motivated by recent results on the minimization of hydrodynamic damping for transversely oscillating flat plates, we conduct a detailed qualitative and quantitative experimental investigation of the flow physics created by the presence of the flanges, that is, the vertical segments in the plate cross section. Specifically, the main goal is to elucidate the effect of flange size on various aspects of fluid–structure interaction, by primarily investigating the dynamics of vortex shedding and convection. We perform particle image velocimetry experiments over a broad range of oscillation amplitudes, frequencies, and flange size-to-width ratios by leveraging the identification of pathlines, vortex shedding and dynamics, distinctive hydrodynamic regimes, and steady streaming. The fundamental contributions of this work include novel hydrodynamic regime phase diagrams demonstrating the effect of flange ratio on regime transitions, and in the investigation of their relation to qualitatively distinct patterns of vortex–vortex and vortex–structure interactions. Finally, we discuss steady streaming, identifying primary, and secondary structures as a function of the governing parameters.