In this paper, fluid-structure interactions of a NACA 0012 airfoil mounted with short flexible membrane(s) and its coupling effect on airfoil aeroacoustics are presented. A time-domain direct aeroacoustic simulation coupled with structural dynamics is carried out at a low Reynolds number of 50,000 to explore the aeroacoustic-structural interactions. Two different airfoil configurations based on single and dual membranes are analyzed. The membrane deflections and their impact on the flow field are characterized in wavenumber-frequency domain to analyze the structural dynamics due to flow unsteadiness within the laminar boundary layer and the resulting acoustic waves emanating from the airfoil trailing edge. A strong correlation between the membrane displacement and downstream propagating flow is observed for all configurations whereas the correlation is considerably weakened between the membrane displacement and upstream acoustic waves which ultimately results in the airfoil self-noise reduction without affecting the airfoil aerodynamics. The extent of noise reduction for dual membrane airfoil configuration is observed to be considerably higher than the single membrane airfoil configuration which corresponds to a much lower correlation among the upstream propagating acoustic waves and membrane deflection for both the membranes and redistribution of upstream flow energy into different frequencies.