The hypotheses of the Karman-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Th...The hypotheses of the Karman-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Karman equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such ns, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered.展开更多
On the basis of the Kármán Donnell theory of thin shells with large deflections and the Boltzmann laws for linear viscoelastic materials, the mathematical model for viscoelastic open shallow shells was formu...On the basis of the Kármán Donnell theory of thin shells with large deflections and the Boltzmann laws for linear viscoelastic materials, the mathematical model for viscoelastic open shallow shells was formulated. By using the Galerkin average method, the original integro partial differential dynamic system was simplified as a integro ordinary differential dynamic system, which can be transformed into a ordinary differential dynamic system by introducing new variables. The dynamical behavior was studied by some classical methods. Dynamical properties, such as, chaos, strange attractor, limit cycle etc., were discovered.展开更多
Applying the wavenumber frequency transfer function to describe the whole system including tht elastic cylindrical shell and the fluid loading, a general expression of the cross spectrum of the interior noise induced ...Applying the wavenumber frequency transfer function to describe the whole system including tht elastic cylindrical shell and the fluid loading, a general expression of the cross spectrum of the interior noise induced by the TBL (turbulent boundary layer) pressure fiuctuations is derived. There are two production mechanisms of the noise: one is direct transfer of the convective ridge of the pressure fluctuations through the shell, the other is the reradiation of resonance modes excited by the pressure fluctuations. At low frequencies the noise produced by the latter mechanism is dominant. Solving the frequency equation of the cylindrical shell with liquid loading, the two Stoneley-type poles in the complex K plane are presented. They are the major sources of the reradiation of shell at low frequencies. Finally, effects of the shell radius, shell thickness, absorption of material and the flow speeds on the noise reduction are computed by numerical iniegration.展开更多
Finite hydrophone and hydrophone array are the wave vector filter and can re-duce the flow noise. In this paper the responses of the cylindrical area hydrophone and two-circular area hydrophone within viscoelastic cyl...Finite hydrophone and hydrophone array are the wave vector filter and can re-duce the flow noise. In this paper the responses of the cylindrical area hydrophone and two-circular area hydrophone within viscoelastic cylindrical shell to the TBL (turbulent boundary layer) pressure fluctuations are investigated. Applying the method based on the wavenumber frequency spectrum analysis, the expressions of 1) the noise power spectrum of a single hy-drophone; 2) the space correlation of two hydrophones; 3) the noise power spectrum of array are derived. The dependencies of the noise reduction on hydrophone shape, dimension, element amount and separation of hydrophones of array are calculated by numerical integration. The wide-band and narrow-band correlation for two hydrophones is also calculated. The numerical results show that hydrophone array can effectively reduce the interior noise.展开更多
In this paper,a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic medium.For small oscillations of incl...In this paper,a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic medium.For small oscillations of inclusion,the problem of heat exchange between a gas,a liquid phase,a viscoelastic shell,and an elastic medium is solved.The energy integral is determined.In the case of small disturbances,the dispersion relation is found from the Rayleigh-Lamb equations,energy,and the known wave equation for the bubbly medium.An analytical expression of the equilibrium speed of sound is written out and its dependence on the size of the viscoelastic shell and the disturbance frequency is established.An example of a mixture of polydimethylsiloxane with air bubbles coated with a rubber shell illustrates the influence of the elasticity of the carrier medium and the shell of the bubbles on the dependence of the phase velocity and attenuation coefficient on the perturbation frequency.For a mixture of water with air bubbles coated with a rubber shell,the influence of the dependences of the shear modulus and viscosity of butyl rubber on the frequency of disturbances at different temperature on the dispersion curves is shown.A comparison of the theory with experimental data is given.展开更多
基金国家自然科学基金，Development Foundation of Shanghai Municipal Commission of Education，上海市科委资助项目，上海市博士后科研项目
文摘The hypotheses of the Karman-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Karman equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such ns, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered.
基金the Development Foundation of Shanghai Municipal Commission of Education (99A01)
文摘On the basis of the Kármán Donnell theory of thin shells with large deflections and the Boltzmann laws for linear viscoelastic materials, the mathematical model for viscoelastic open shallow shells was formulated. By using the Galerkin average method, the original integro partial differential dynamic system was simplified as a integro ordinary differential dynamic system, which can be transformed into a ordinary differential dynamic system by introducing new variables. The dynamical behavior was studied by some classical methods. Dynamical properties, such as, chaos, strange attractor, limit cycle etc., were discovered.
文摘Applying the wavenumber frequency transfer function to describe the whole system including tht elastic cylindrical shell and the fluid loading, a general expression of the cross spectrum of the interior noise induced by the TBL (turbulent boundary layer) pressure fiuctuations is derived. There are two production mechanisms of the noise: one is direct transfer of the convective ridge of the pressure fluctuations through the shell, the other is the reradiation of resonance modes excited by the pressure fluctuations. At low frequencies the noise produced by the latter mechanism is dominant. Solving the frequency equation of the cylindrical shell with liquid loading, the two Stoneley-type poles in the complex K plane are presented. They are the major sources of the reradiation of shell at low frequencies. Finally, effects of the shell radius, shell thickness, absorption of material and the flow speeds on the noise reduction are computed by numerical iniegration.
文摘Finite hydrophone and hydrophone array are the wave vector filter and can re-duce the flow noise. In this paper the responses of the cylindrical area hydrophone and two-circular area hydrophone within viscoelastic cylindrical shell to the TBL (turbulent boundary layer) pressure fluctuations are investigated. Applying the method based on the wavenumber frequency spectrum analysis, the expressions of 1) the noise power spectrum of a single hy-drophone; 2) the space correlation of two hydrophones; 3) the noise power spectrum of array are derived. The dependencies of the noise reduction on hydrophone shape, dimension, element amount and separation of hydrophones of array are calculated by numerical integration. The wide-band and narrow-band correlation for two hydrophones is also calculated. The numerical results show that hydrophone array can effectively reduce the interior noise.
文摘In this paper,a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic medium.For small oscillations of inclusion,the problem of heat exchange between a gas,a liquid phase,a viscoelastic shell,and an elastic medium is solved.The energy integral is determined.In the case of small disturbances,the dispersion relation is found from the Rayleigh-Lamb equations,energy,and the known wave equation for the bubbly medium.An analytical expression of the equilibrium speed of sound is written out and its dependence on the size of the viscoelastic shell and the disturbance frequency is established.An example of a mixture of polydimethylsiloxane with air bubbles coated with a rubber shell illustrates the influence of the elasticity of the carrier medium and the shell of the bubbles on the dependence of the phase velocity and attenuation coefficient on the perturbation frequency.For a mixture of water with air bubbles coated with a rubber shell,the influence of the dependences of the shear modulus and viscosity of butyl rubber on the frequency of disturbances at different temperature on the dispersion curves is shown.A comparison of the theory with experimental data is given.
