Study Of The Sound Propagation In The Curved Pipe

Pipe is regarded as an important material transportation carrier,which is widely used in various industries.When the pipe is curved,the pipe segment is rotational symmetry no longer,and the inner pipe propagation process becomes complicated,the normal modes will be mutual conversion,therefore,studying the sound propagation in curved pipes becomes significant.This paper first describes the formation the basic theory of normal mode in the long straight pipes,which is under the circumstance of the absolutely hard boundary conditions.Then we obtained and analyzed the velocity potential equations of normal modes,after which we studied the reason of pipe wave attenuation.Based on this,derived different local oscillator excitation cutoff frequency of the various normal modes' amplitude values each order normal modes.Using the cross-section approximation method focuses on and derives the relevance coefficient of different normal modes when pipe is curved.Then we approximate the differential equations of the normal modes between waves,besides,we simulate the relevance coefficient by MATLAB.By the differential equations,we obtain the coefficient of velocity potential equations,and discuss the factors which affects the relevance coefficient and the coefficient of velocity potential equations,simulating the relevance coefficient,the coefficient of velocity potential equations and listing the order relevance coefficient between the normal modes were followed.We analyzed and verified conversion on the principle of normal modes in the polar coordinate system,studying the basic principle of pulse wave propagation in the pipe.In addition,we introduced the phase velocity and the group velocity equation in the dispersion medium.Based on the theory,using the control variable method,parameters experiments were carried out.Confirm the different normal modes from time and space domain.Then measured the waveform in different positions of the sections cut before and after the curved pipe,after which we drawed or computed the vibration amplitude distribution map of the section.Furthermore,confirmed the type of the normal modes.Affecting factors of the relevance coefficient and sound pressure were studied,the results were processed by MATLAB which was used the results of the experiments to modify the model,then we summarized and analyzed normal modes wave propagation in curved pipes which can provide numerical reference of sound propagation characteristics in curved pipe,at last,we make conclusion.