It is proposed to present appropriate variational formulations for linear vibration of elastic structure coupled with an internal inviscid, homogeneous, compressible fluid (liquid or gas), gravity effects being discarded in the presence of a free surface. Hybrid passive/active damping treatments will be investigated for noise and vibration reduction problems. It should be noted that generally, active structural treatments (using for example piezoelectric smart materials) are effective in the low frequency range, while passive structural treatments (such as viscoelastic materials, porous insulation...) are effective for higher frequency domain.