Characteristics Of Power Flow And Sound Radiation In Submerged Complex Cylindrical Shells

The work of this paper is one part of the research project"Calculation of Structural Sound Transmission and Sound Radiation of Submerged Structure"which was supported by foundation of national key project in"the State 10th Five-Year Plan"(Contract No.10105010204). Using periodic structure theory and vibrational power flow method, the characteristics of vibrational power flow and sound radiation in an infinite submerged periodic ring-stiffened cylindrical shell, a submerged infinite cylindrical shell reinforced by doubly periodic supports of rings and bulkheads, a submerged infinite unconstrained viscoelastic cylindrical shell, are studied by both analysis and experiment, respectively. The influences of different structural parameters such as ring, bulkhead, viscoelastic damping layer, etc, are discussed detailedly. The analytic model is close to engineering practice, and it will provide reliable calculated method for the design of new type and high performance submarine with small vibrational response and low radiated noise level.First, vibrational power flow and sound radiation in an infinite submerged periodic ring-stiffened cylindrical shell are considered. Periodic structure theory and vibrational power flow method are introduced into the cylindrical shell-fluid coupled system. The harmonic motion of the shell and the pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively, and the coupling condition on the outer surface of the shell wall is considered. The influences of the ring are replaced by the exerting forces and moments on the shell. Space-harmonic analysis is used to deduce the responses of the coupled system excited by a driving force. The forces and moments of the shell are derived by infinitesimal stress and stress-strain relationship, and then the calculated formulas of input power flow, propagation power flow as well as sound radiation can be obtained. In the numerical calculation, the influences of frequency, circumferential order number, structural damping and ring parameters on the results are discussed, respectively, and the comparison are made with those of vacuum stiffened shell and fluid-filled stiffened shell.Then, the researched object is extend to doubly periodic coupled system, and vibrational power flow and sound radiation in a submerged cylindrical shell reinforced by doubly periodic supports of rings and bulkheads are investigated. The dispose of the bulkhead is similar to that of the ring, and space-harmonic analysis is used once again to deduce the responses of the doubly periodic coupled system. The influences of deferent parameters, especially bulkhead parameters on the results are discussed, respectively.Due to the extensive application of viscoelastic damping material, vibrational power flow and sound radiation in a submerged infinite unconstrained viscoelastic cylindrical shell are also studied. The harmonic motion of the shell and the pressure field in the fluid are described by Flügge shell equations and Helmholtz equation, respectively. The damping characteristics are considered by complex modulus method, and the solutions are obtained by wave propagation approach. Among the numerical results, the discussions concentrate on the influences of viscoelastic damping layer.The theory of periodic structure and the method of power flow have been developed. Space-harmonic analysis method is firstly employed to analysis vibrational power flow and sound radiation in the submerged periodic and doubly periodic coupled system. The characteristics of vibrational power flow and sound radiation are also investigated for a viscoelastic cylindrical shell immersed in the fluid. In experiment, the model of a periodic ring-stiffened cylindrical shell is designed. Both the power flow into a cylindrical shell immersed in the fluid and the radiated sound pressure of the model underwater are measured. Comparison between experiment results and theoretical predictions verifies the validity of the theoretical method in this paper.The vibration and noise in the structure will propagate to a far location by means of waves, the essence of which is the propagation of power flow, and the radiated sound power is equal to the residual of loss energy caused by damping deducted from the input power flow. In addition, the response of unbounded structure is approximately equal to the average of that of bounded structure at low frequency, and the responses of two kinds of structures drive to coincidence with the increasing of frequency. So, the results presented here will be helpful to reduce vibration and noise of submarine and other structure.