Fig. 1 Infinite double concentric large cylindrical shells with periodic bulkheads and cavities submerged in the water More

Fig. 2 Positive loading directions of the reactive forces at the inner and outer edges of the annular bulkhead More

Fig. 3 SPL comparisons of the present method, analytical model, and experimental measurements: ( a ) θ = 0 and ( b ) θ = π /4 More

Fig. 4 Partial and total sound pressure power spectra of inner cylindrical shell at 2kHz: ( a ) total sound pressure power spectra of inner cylindrical shell calculated by u ~ 3 ( i ) and u ~ 3 ( o ) , ( b ) partial sound pressure power spectra of inner... More

Fig. 5 Partial and total sound pressure power spectra of outer cylindrical shell at 2kHz: ( a ) sound pressure power spectra of outer cylindrical shell on the bottom cylindrical surface calculated by u ~ 3 ( i ) and u ~ 3 ( o ) , ( b ) partial sound pre... More

Fig. 6 Sound pressure power spectra of the cylindrical interface between the outer cylindrical shell and external free fluid at 4 kHz: ( a ) a 1 = 1.5 m, a 2 = 5 m and ( b ) a 1 = 4.4 m, a 2 = 5 m More

Fig. 7 Sound pressure power spectra of stiffened double cylindrical shells on the interface between the outer cylindrical shell and external free fluid at 2 kHz: ( a ) without annular fluid, ( b ) with annular fluid, and ( c ) with acoustic cavities More

Fig. 8 Sound pressure power spectra of stiffened double cylindrical shells with acoustic cavities on the two fluid–solid coupling interfaces of annular fluid at 2 kHz: ( a ) sound pressure power spectra of the inner cylindrical shell and ( b ) sound pressure power spectra of the outer cylindrical ... More

Fig. 9 Sound pressure power spectra of stiffened double cylindrical shells on the cylindrical interfaces between outer cylindrical shell and external free fluid at 4 kHz: ( a ) without annular fluid, ( b ) with annular fluid, and ( c ) with periodic cavities More

Fig. 10 Sound pressure power spectra of stiffened double cylindrical shells on the two fluid–solid interfaces among inner cylindrical shell, annular cavities, and outer cylindrical shell at 4 kHz: ( a ) sound pressure power spectra of inner cylindrical shell and ( b ) sound pressure power spectra ... More

Fig. 11 Sound pressure power spectra of stiffened double cylindrical shells on the three fluid–solid coupling interfaces for the shell structures, acoustic cavity fluid, and external free fluid at 8 kHz: ( a ) sound pressure power spectra of the inner cylindrical shell, ( b ) sound pressure power ... More

Fig. 12 SPL of stiffened double cylindrical shells without annular fluid, with annular fluid, or with periodic cavities More

Fig. 1 Contours of sound pressure p e in the Sommerfeld–Watson transform More

Fig. 2 Sound pressure directivity of the bare outer cylindrical shells with different radii: ( a ) a 2 = 4.5 m at 10 kHz, ( b ) a 2 = 4.5 m at 16 kHz, ( c ) a 2 = 2.5 m at 10 kHz, and ( d ) a 2 = 2.5 m at 20 kHz More

Fig. 3 Sound pressure directivity of bare outer shells with wall thickness h 2 = 0.04 m: ( a ) a 2 = 1.5 m at 10 kHz and ( b ) a 2 = 1.5 m at 16 kHz More

Fig. 4 Sound pressure directivity of bare outer cylindrical shells given by circumferential harmonic waves at 10 kHz: ( a ) a 2 = 2.5 m and ( b ) a 2 = 1.5 m and h 2 = 0.04 m More

Fig. 5 Sound pressure directivity of bare double cylindrical shells given by p s 1 and p e + defined in Eq. (32) at 16 kHz More

Fig. 6 Sound pressure directivity for the bare double cylindrical shells calculated by p e − and p e + defined in Eq. (20) and p e at 16 kHz More