Vibrational Power Flow And Radiated Sound Power Of Cylindrical Shell In Fluid With Different Theories

The work is a part of the project "Characteristics of Vibrational Power Flow in Submerged Coupled Cylindrical Shell", which is supported by the National Natural Science Foundation of China (Grant No.40976058). By using the classical integral transform technique, potential theory and the higher precision inversion computation, the relations of the infinite cylindrical shell in fluid are investigated using the elasticity Navier equations and then the vibrational power flow and the radiated sound power of infinite damped cylindrical shell, the finite cylindrical shell, the finite damped cylindrical shell and the ring-stiffened cylindrical shell are studied by the elastic Navier equations and Fliigge theory, respectively. The influence of the material parameter of the coated layer to the vibrational power flow and the radiated sound power is discussed detailedly. The model established by Navier equations could be suitable for any frequency and arbitrary thickness of the coated layer, and the results could be helpful to reduce the vibration and noise in practice.By using the lame decomposition, the displacement field of elastic equations is decomposed into irrotational and divergenceless potentials which satisfy the Helmholtz equation. And then substituting the differential operator of cylindrical coordinate system and rectangular coordinate system into the Helmholtz equation, the motion equations of the cylindrical shell and plate could be obtained. For the motion equation of ideal fluid, it only needs to set the lame coefficientμ=0. So the motion equations of fluid and cylindrical shell or plate can be solved similarly.Plate can be considered as a special cylindrical shell with infinity of curvature radius. Through comparing the transfer function of cylindrical shell and plate with different frequencies, it is found that the transfer function of the cylindrical shell tends to the transfer function of plate as the frequency increases (beyond ring frequency). And the bigger of the circumferential mode number of cylindrical shell is, the slower of the tendency is.Then, the vibrational power flow and the radiated sound power of the infinite damped cylindrical shell under circumferential force are investigated. Because the thickness of the damped cylindrical shell may be over the range of thin shell theory, two models are set up. Model 1 is the inner shell and coated layer of the damped cylindrical shell are both described by the Navier equations. Model 2 is the inner shell and coated layer of the damped cylindrical shell described by the Fliigge theory and Navier equations, respectively. In the numerical calcaulation, the influence of the circumferential mode of the cylindrical shell and the influence of material parameter of the coated layer to the vibrational power flow and the radiated sound power are studied detailedly by model 1. In order to check the accuracy and application range of the model 2, the vibrational power flow and the radiated sound power of the two models are also compared with different thickness of the damped cylindrical shell.The infinite cylindrical shell is a simplified model. In fact, the cylindrical shell is finite length in practice structure. Then the vibrational power flow and radiated sound power of the finite (ring-stiffened) cylindrical shell are investigated by Fliigge theory and Navier equations. And the vibrational power flow and the radiated sound power of the finite (ring-stiffened) damped cylindrical shell are studied by the model 1 and model 2. The relation between the infinite and finite cylindrical shell are concluded, and the influence of the geometric parameter and material parameter of the coated layer, and the ribs to the vibrational power flow and the radiated sound power are investigated detailedly.The vibrational power flow and the radiated sound power of infinite (damped) cylindrical shell and finite (damped) cylindrical shell are investigated by Flugge theory, Navier equations and their combined model, respectively. Through comparison the results, the application range is summarized. Besides, the influence of the material parameter of the coated layer to the the vibrational power flow and the radiated sound power is also discussed in detail. So, the results in the paper can be a reference to reduce vibration and noise in practice.