Abstract: A semi-analytical modeling and solving method is proposed for the three-dimensional inserted-pipe muffler with asymmetric impedance boundary conditions and offset inserted-pipes.The experimental curves and finite element analysis results verify the correctness of the theoretical model and corresponding results.The nature frequencies,sound pressure responses and transmission losses are predicted.First of all,the Lagrangian functional of each acoustic subspace in the inserted-pipe muffler is constructed.According to the continuity condition of pressure and particle velocity between acoustic subspaces,the theoretical model of the three-dimensional inserted-pipe muffler is constructed.Then,the sound pressure is expanded into a combined form of Chebyshev-Fourier series and the eigen pairs of the muffler are obtained by using Ritz method.A test rig is set up and the transmission loss tests on mufflers separately with rigid wall or impedance wall are carried out.The effects of several parameters on the performance of muffler are analyzed,including the value of the wall impedance,the area and distribution of the impedance,and the offset of the inserted-pipe.The results show that the proposed method is valid and the reasonable setting of wall impedance in the muffler can effectively reduce the output sound pressure.