This paper presents an approximate analytical model for estimating the transmission loss (TL) of a finite rectangular plate in the low frequency range, which is based on the modal summation approach (MSA) taking into account the modal radiation impedance and fluid loading. The mode-dependent radiation resistance is calculated using the Rayleigh integral. The fluid loading is taken into account through the natural frequency modified by the added mass. The results are compared with the ones of Statistical Energy Analysis (SEA) coupled with FEM and FEM coupled with BEM. In addition, the effects of the various vibration modes and the fluid loading on TL, and a way for reducing the calculation time are discussed.

An approach is presented to form and broaden the low-frequency band gap of the double panel structure (DPS) by using a locally resonant sonic crystal (LRSC) in this work. The LRSC is made of cylindrical Helmholtz resonators arranged on square lattice. Their designs are similar to a slot-type resonator, but have different depths of slot. Elongating the slit neck inward and distributing the depths of slots produce a broad local resonant band gap at low frequencies: an average insertion loss (IL) of 10.9 dB covering 520 Hz to 1160 Hz with a LRSC of 12 cm width. Next, the effect of porous material filled into the resonators on the local resonant band gap is evaluated. It is shown that filling of porous material into the resonators decreases the height and width of the local resonant band gap. Finally, the transmission losses (TLs) through the DPS with LRSC are calculated as a function of the incident angle of the sound wave for LRSC embedded in porous material and not. The results show that the porous material can be significantly reduce the incident angle dependency of TL through the DPS with LRSC.