The insertion loss of acoustic radiation of damped cylindrical shell described by 3-D elasticity Navier equations under radial harmonic applied load in fluid is presented. The classical integral transform technique, p...The insertion loss of acoustic radiation of damped cylindrical shell described by 3-D elasticity Navier equations under radial harmonic applied load in fluid is presented. The classical integral transform technique, potential theory and Lamè resolution are used to derive the solutions of Navier equations. The higher precision inversion computation is introduced to solve the linear equations. Comparing with acoustic radiation of one-layer cylindrical shell, the influence of thickness, mass density, dilatational wave loss factor and Young's modulus of damping material and circumferential mode number of the cylindrical shell on the insertion loss is concluded. The theoretical model in the paper can be used to deal with the arbitrary thickness and any frequency of the coated layer in dynamic problem. The conclusions may be of theoretical reference to the application of damping material to noise and vibration control of submarines and underwater pipes.展开更多
The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this pa...The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this paper.In a paper(Comm.Pure Appl.Math.,46,1993,621-665) by Z.P.Xin,the author constructed a sequence of solutions to one-dimensional Navier-Stokes isentropic equations converging to the rarefaction wave as the viscosity tends to zero.Furthermore,he obtained that the convergence rate is ε 1/4 | ln ε|.In this paper,Xin's convergence rate is improved to ε1/3|lnε|2 by different scaling arguments.The new scaling has various applications in related problems.展开更多
文摘The insertion loss of acoustic radiation of damped cylindrical shell described by 3-D elasticity Navier equations under radial harmonic applied load in fluid is presented. The classical integral transform technique, potential theory and Lamè resolution are used to derive the solutions of Navier equations. The higher precision inversion computation is introduced to solve the linear equations. Comparing with acoustic radiation of one-layer cylindrical shell, the influence of thickness, mass density, dilatational wave loss factor and Young's modulus of damping material and circumferential mode number of the cylindrical shell on the insertion loss is concluded. The theoretical model in the paper can be used to deal with the arbitrary thickness and any frequency of the coated layer in dynamic problem. The conclusions may be of theoretical reference to the application of damping material to noise and vibration control of submarines and underwater pipes.
基金supported by the National Natural Science Foundation of China for Outstanding Young Scholars(No. 10825102)the National Basic Research Program of China (973 Program) (No. 2011CB808002)
文摘The zero dissipation limit for the one-dimensional Navier-Stokes equations of compressible,isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions is investigated in this paper.In a paper(Comm.Pure Appl.Math.,46,1993,621-665) by Z.P.Xin,the author constructed a sequence of solutions to one-dimensional Navier-Stokes isentropic equations converging to the rarefaction wave as the viscosity tends to zero.Furthermore,he obtained that the convergence rate is ε 1/4 | ln ε|.In this paper,Xin's convergence rate is improved to ε1/3|lnε|2 by different scaling arguments.The new scaling has various applications in related problems.
