Nonlinear Pressure Wave Analysis by Concentrated Mass Model:(3rd Report, Modeling of Enlargement and Contraction Element)

A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effects in the propagation medium. The purpose of this study is to establish a practical analytical model to analyze this phenomenon. In previous reports, a concentrated mass model was proposed to analyze nonlinear pressure wave phenomena in a straight cylindrical tube. In the present paper, models of enlargement and contraction are proposed. The models of the enlargement and contraction elements consist of masses, nonlinear springs, base support dampers, and nonlinear dampers. The nonlinear damper is derived from the pressure loss at the enlargement and contraction. To confirm the validity of the proposed model, an experiment on a sound tube with an expansion-chamber muffler is performed and the experimental results are compared with the numerical results obtained by the concentrated mass model. The numerical computational results agree well with the experimental result. Therefore, it is concluded that the proposed enlargement and contraction models are valid for the numerical analysis of nonlinear pressure wave problem in a tube with an expansion-chamber muffler.