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To reduce low-frequency noise of the water-filled pipeline system,a compact flexible micro-perforated muffler with a flexible back cavity(FMPMFBC)is proposed.The flexible pipe wall is made of a rubber-cord composite material.A numerical solution for the transmission loss is derived.Firstly,the flexible micro-perforated panel(FMPP)is equivalent to a flexible porous material based on Biot-Allard porous-elastic theory.Then,a periodic structural unit of the aramid fabric cloth is established with the two-scale method,and the equivalent stiffness matrix is obtained.Besides,a multi-layer composite model for the flexible pipe wall is constructed according to the lamination theory.Coupling with the internal sound field,the transmission loss of the FMPMFBC is calculated.On a water-filled impedance tube,the transmission loss curves of the FMPMFBC prototypes are measured with the two source-location method,and compared with those of a flexible micro-perforated muffler with a rigid back cavity(FMPMRBC)and an expansion muffler.Theoretical results are experimentally verified.The FMPMFBC is a hybrid muffler combining reflection with dissipation,capable of attenuating broadband low-frequency noise.The transmission loss of prototype B2 in the frequency bands of[40 300]Hz and[40 1200]Hz is 36 dB and 30 dB,respectively,while the transmission loss of the same-sized expansion muffler in the corresponding frequency bands is 7 dB and 11 dB,respectively.