Xiang Zhu

Propeller Excitation of Longitudinal Vibration Characteristics of Marine Propulsion Shafting System

The submarine experiences longitudinal vibration in the propulsion shafting system throughout most of run. A transfer matrix model of the propulsion shafting system, in which the dynamic characteristics of oil film within thrust bearing are considered, is established to describe the dynamic behavior. Using hydrodynamic lubrication theory and small perturbation method, the axial stiffness and damping of oil film are deduced in great detail, followed by numerical estimation of the foundation stiffness with finite element method. Based upon these values of dynamic parameters, the Campbell diagram describing natural frequencies in terms of shafting rotating speeds is available, and the effect on the 1st natural frequency of considerable variations in thrust bearing stiffness is next investigated. The results indicate that the amplitude of variation of the 1st natural frequency in range of low rotating speeds is great. To reduce off-resonance response without drastic changes in propulsion shafting system architecture, the measure of moving thrust bearing backward is examined. The longitudinal vibration transmission through propulsion shafting system results in subsequent axial excitation of hull; the thrust load acting on hull is particularly concerned. It is observed that the measures of structural modification are of little benefit to minimize thrust load transmitted to hull.

The Vibro-Acoustic Characteristics of the Cylindrical Shell Partially Submerged in the Fluid

The characteristics of the sound radiation and vibrational power flow of the partially submerged cylindrical shell under a harmonic excitation are studied. The approximate acoustic boundary of the free surface is used to solve the fluid domain. The structure-fluid coupling equation is established based on the Flügge and Helmholtz theories. The far-field sound pressure is calculated and compared with that in infinite field. It is found that the far-field sound pressure presents large gap in different immersion status in the presence of the free surface while the results of the input power flow in these cases have less differences.

Free Vibration Analysis of Fluid-Filled Elliptical Cylindrical Shells

A method is presented for the free vibration analysis of finite fluid-filled elliptical cylindrical shells with variable curvature. Based on the Goldenveizer thin-shell theory, the vibration equations have been expressed as a matrix differential equation by using the transfer matrix and the fluid-loading term is represented as the form of Mathieu function, the transfer matrix is determined by use of the mid-Magnus series method. The natural frequencies are calculated numerically in terms of the matrix elements with a combination of appropriate initial guess and Lagrange interpolation method. The results of the degradation model obtained by the present method are compared to those of existing literatures. It is shown that the present method is highly accurate and the results are reliable. The sensitivity of the frequency parameter to the ellipticity parameter and the length of the shell are investigated respectively.

Far-field acoustic radiation and vibration of a submerged finite cylindrical shell below the free surface based on energy functional variation principle and stationary phase method

The far-field acoustic radiation and vibration of a submerged finite cylindrical shell below the free surface are studied. Based on the energy functional variation principle, the image method and the Grafs addition theorem, the structureâ–“acoustic coupling vibration equation for the cylindrical shell is established. The far-field sound pressure expressions of the cylindrical shell are obtained by using the Fourier transform and the stationary phase method. The reliability and efficiency of the proposed analytical method are validated by comparison with the finite element method and the boundary element method. It is found that the presence of the free surface increases the natural frequencies of the same orders compared to those without the free surface. When the cylindrical shell is closed to the free surface, the circumferential mode shapes become very different from those in infinite fluid. However, the free vibration and forced vibration characteristics of the cylindrical shell below the free surface become consistent with those in infinite fluid when the submerged depth exceeds severalfold radiuses. The far-field sound pressure of the cylindrical shell below the free surface is very different from that in infinite fluid even though the submerged depth is relatively large. Moreover, the directivity of the far-field sound pressure of the cylindrical shell is similar to that of the acoustical dipole due to the free surface. Based on energy functional variation principle and stationary phase method, the proposed method provides an alternative for vibroacoustic problem of elastic structures bounded by acoustic boundary with good accuracy and applicability.

An Analytical Solution for Free Flexural Vibration of a Thin Cylindrical Shell Submerged in Acoustic Half-Space Bounded by a Free Surface

An analytical solution is proposed for the free flexural vibration of a finite cylindrical shell submerged in half-space bounded by a free surface in the low frequency range. The motion of the shell is described by the Flugge shell theory and the fluid surrounding the shell is assumed to be an acoustic media. The free surface effect is considered by satisfying the pressure release boundary condition. The accuracy of the present method is verified through comparison with the finite element solution. To throw light on the influence mechanism of free surface on the coupled modal frequencies, a modal added mass is introduced and calculated. Numerical results show that when the shell is close to the free surface, the presence of free surface will make a negative contribution to the modal added mass and finally result in the corresponding increase of the coupled modal frequencies. But the free surface effect will decrease when the immersion depth of the cylindrical shell increases. Finally, the free surface effect can be neglected if the immersion depth is higher than four times the shell radius. This conclusion is helpful to select proper test environment for an experiment on the dynamic characteristics of submerged cylindrical shells.

Vibration Characteristics Research of Finite Cylindrical Shells Semi-Submerged

A significant amount of research on the vibration and sound radiation of the cylindrical shell has been carried out and reported. The cylindrical shell was usually assumed to be submerged in an infinite fluid. However, the fluid region surrounding the cylindrical shell is bounded. Free vibration and forced vibration characteristics of finite cylindrical shells semi-submerged are studied in this paper, based on energy functional variational principle. The combined form of the triangular series and the Fourier series is used for the displacement of the cylindrical shell, then the orthogonality can be used to eliminate the other two directions after the variation, and only the radial displacement is kept. The relationships between the amplitudes of fluid load and the amplitudes of the radial displacement are established by the orthogonal processing of the continuous conditions of the solid-liquid coupling contact surface and the boundary conditions of the free liquid surface. Finally, the fluid structure coupling control equation is obtained. The results show that the method is correct and effective, in addition, providing a new thought for solving similar problem.

Vibrational Frequencies Calculation of Fluid Conveying Pipes Based on Fluid-Structure Coupling and Acoustic-Structure Coupling Models

Two coupling models, the fluid-structure coupling and the acoustic-structure coupling, have been studied in this paper, in order to describe the free vibration of a fluid-filled cylindrical shell under internal pressure from two different angles. For both models, a new approach to solve the characteristic equation is presented, using the Galerkin method to obtain the natural frequency of each mode. The comparison shows the results of two models are in good agreement. Although the two models are based on different mechanical theories, the mathematic essences are confirmed to be the same, both derived from Bessel functions.

Nonlinear Input Power Flow Analysis of a Plate with a Breathing Crack

Plates are commonly used in engineering structures. However crack is the most common form of damages in the plate structures. The crack in the plate will open and close during vibrational cycle, making the cracked structure with nonlinear dynamic characteristics. Based on vibrational power flow theory, the nonlinear dynamic analysis of a plate structure is carried out. The contact elements are used to simulate the nonlinear behavior of the breathing crack. Aiming to study the input power characteristics and the super harmonic resonance of a breathing cracked plate which is under the resonant excitation. By the finite element calculation, the structural input power curve is analyzed, which provides a theoretical basis for the damage identification of cracked structures.

Hydrodynamic and Noise Characteristics Analysis of a Sea Valve and its Optimization

The sea valve is a critical unit in the seawater pipelines onboard. Its mainly used to control and adjust the flux of seawater. In the practical use, the vibration and sound level of a kind of valve is proved to be too high to maintain the acoustic performance of ships.In this paper, the three-dimensional geometry and CFD model of a typical sea valve is established.Then the flow fields inside the valve, flow characteristics, drag reduction characteristics and noise characteristics were analyzed, as well as the fluid-solid coupling response between the flow field and the valve structure. Based on the analysis, two optimum schemes are proposed in order to improve the flow characteristics of the flow field and reduce vibration and noise level of this type of sea valves. The calculated results show that two optimum schemes both can improve the hydrodynamic and noise characteristics, and the scheme two is relatively better.

Structural Strength Analysis of Main Crane Pedestal of the Jack-Up Wind Turbine Installation Vessel

The jack-up wind turbine installation vessel is a special kind of vessel for building the offshore wind power farm. The main crane pedestal, which is the supporting structure of the crane on the main deck of the vessel, is always under high level loads when the ship is in operation condition. In this paper, the structural strength analysis of main crane pedestal of the jack-up wind turbine installation vessel was presented. The direct calculated method was used to evaluate the strength of the main crane pedestal. The FE model of main crane pedestal was established with refined mesh, and the adjoining hull structure was also modeled to provide accurate boundary condition. Considering the permanent loads, variable loads (crane loads) and wind loads on the pedestal, the load combinations were defined for the ultimate limit state for every 45 degree. The deformation and stress of the pedestal and the hull structures were calculated and checked. The results showed that all stress results were within the maximum allowable stresses. The critical areas are often located at the link region of hull and pedestal.