Broadband noise reduction over the low-mid frequency range in the building and transportation sectors requires compact lightweight sound absorbers of typical sub-wavelength size. The use of multi-layered closely-spaced (micro-)perforated membranes or panels, if suitably optimized, contribute to these objectives. However, their elasticity or modal behaviors often impede the final acoustical performance of the partition. The objective of this study is to get insights into the vibrational effects induced by elastic limp membranes or panels volumetric modes on the optimized sound absorption properties of acoustic fishnets and functionally-graded partitions (FGP). Cost-efficient global optimization of the partition total frequency-averaged dissipation is achieved from simulated annealing with vibrational effects included through an impedance translation method. Critical coupling analysis reveals how the membranes or panels vibrations redistribute the locations of the Hole-Cavity resonances as well as their cross-coupling with the panels first volumetric mode. It is found that elastic limp micro-perforated membranes broaden the first pass-band of acoustic fishnets while smoothing out the dissipation ripples over the FGP optimiza-tion bandwidth. Moreover, the resonance frequency of the first panels mode sets an upper limit to the broadband optimization of FGPs, up to which high dissipation, low reflection and low trans-mission can be achieved.