Tianyun Li

Far-field sound radiation of a submerged cylindrical shell at finite depth from the free surface

The far-field sound radiation behavior of a circular cylindrical shell submerged at finite depth from the free surface is studied. Based on the Flügge shell theory and the Helmholtz equation, the structure-acoustic coupling equation is established. An image method is applied so that the sound boundary condition of the free surface can be satisfied. Analytical expression of the far-field sound pressure is obtained using the stationary phase method and the Grafs addition theorem. In order to evaluate the effect of the submerged depth on sound radiation, the results of the submerged cylindrical shell at finite depth from the free surface are compared with those of the submerged cylindrical shell in the infinite fluid. The characteristics of the far-field sound pressure with the change of the depth are investigated. It is found that the submerged depth has a significant influence on the far-field sound pressure radiated from the submerged cylindrical shell due to the free surface effects. The work provides more understanding on the sound radiation properties of the submerged circular cylindrical shell without assuming infinite fluid field, which was commonly used in previous studies.

Application of Smoothed Finite Element Method to Two-Dimensional Exterior Problems of Acoustic Radiation

In this work, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems. The SFEM-Q4 can be regarded as a com...

Hybrid gradient smoothing technique with discrete shear gap method for shell structures

Abstract In order to enhance the performance of the discrete shear gap technique (DSG) for shell structures, the coupling of hybrid gradient smoothing technique (H-GST) with DSG using triangular elements (HS-DSG3) is presented to solve the governing partial differential equations of shell structures. In the formulation HS-DSG3, we firstly employ the node-based gradient smoothing technique (N-GST) to obtain the node-based smoothed strain field, then a scale factor α ∈ [ 0 , 1 ] is used to reconstruct a new strain field which includes both the strain components from standard DGS3 and the strain components from node-based smoothed DSG3 (NS-DSG3). The HS-DSG3 takes advantage of the “overly-soft” NS-DSG3 model and the “overly-stiff” DSG3 model, and has a relatively appropriate stiffness of the continuous system. Therefore, the degree of the solution accuracy can be improved significantly. Several typical benchmark numerical examples have been investigated and it is demonstrated that the present HS-DSG3 can provide better numerical solutions than the original DSG3 for shell structures.

SPH Simulation of Acoustic Waves: Effects of Frequency, Sound Pressure, and Particle Spacing

Acoustic problems consisting of multiphase systems or with deformable boundaries are difficult to describe using mesh-based methods, while the meshfree, Lagrangian smoothed particle hydrodynamics (SPH) method can handle such complicated problems. In this paper, after solving linearized acoustic equations with the standard SPH theory, the feasibility of the SPH method in simulating sound propagation in the time domain is validated. The effects of sound frequency, maximum sound pressure amplitude, and particle spacing on numerical error and time cost are then subsequently discussed based on the sound propagation simulation. The discussion based on a limited range of frequency and sound pressure demonstrates that the rising of sound frequency increases simulation error, and the increase is nonlinear, whereas the rising sound pressure has limited effects on the error. In addition, decreasing the particle spacing reduces the numerical error, while simultaneously increasing the CPU time. The trend of both changes is close to linear on a logarithmic scale.

Edge-Based Smoothed Three-Node Mindlin Plate Element

AbstractThe edge-based smoothed finite element method (ES-FEM) was proposed recently to improve the accuracy of the standard finite element method for solid mechanics. In the present paper, the ES-FEM is incorporated with the three-node Mindlin plate element (MIN3) to give a novel edge-based smoothed MIN3 (ES-MIN3) for plate analysis. The system stiffness matrix is computed by employing the edge-based strain smoothing technique over the edge-based smoothing domain. For the purpose of avoiding the transverse shear-locking, the MIN3 element is performed to calculate the strains in each element. From a series of selected numerical examples, it is found that the present ES-MIN3 possesses highly accurate solutions, and can be competitive with many existing plate elements.

The prediction of the elastic critical load of submerged eccentric cylindrical shell based on vibro-acoustic model

Abstract An effective new approach to nondestructively predict the elastic critical hydrostatic pressure of a submerged eccentric cylindrical shell is presented in this paper. According to the geometry characteristic of the cross section of eccentric cylindrical shell, the eccentric problem is transformed into the problem of variable thickness in the circumferential direction. The vibration equations considering hydrostatic pressures of outer fluid are written in the form of a matrix differential equation which is obtained by using the transfer matrix of the state vector of the shell. Depending on wave propagation approach, the data of the fundamental natural frequencies of the shell with various eccentricities under different hydrostatic pressure and boundary conditions are obtained by solving the frequency equation with a Lagrange interpolation method. The curve of the fundamental natural frequency squared versus hydrostatic pressure is then drawn with the data, which is approximately straight line or parabola that depends on the eccentric value. The elastic critical hydrostatic pressure is therefore obtained while the fundamental natural frequency is assumed to be zero according to the curve. The results obtained by the present approach show good agreement with published results and finite element results.

Application of smoothed finite element method to acoustic scattering from underwater elastic objects

In this work, the smoothed finite element method (S-FEM) is employed to solve the acoustic scattering from underwater elastic objects. The S-FEM, which can be regarded as a combination of the standard finite element method (FEM) and the gradient smoothing technique (GST) from the meshless methods, was initially proposed for solid mechanics problems and has been demonstrated to possess several superior properties. In the S-FEM, the smoothed gradient fields are acquired by performing the GST over the obtained smoothing domains. Due to the proper softening effects provided by the gradient smoothing operations, the original “overly-stiff” FEM model is softened and the present S-FEM possesses a relatively appropriate stiffness of the continuous system. Therefore, the quality of the numerical results can be significantly improved. The numerical results from several typical numerical examples demonstrate that the S-FEM is quite effective to handle acoustic scattering from underwater elastic objects and can provi...

An edge-based smoothed finite element method for two-dimensional underwater acoustic scattering problems

An edge-based smoothed finite element method (ES-FEM) is presented that cures the overly-stiff property of the original standard finite element method (FEM) for the analysis of two-dimensional underwater acoustic scattering problems. In the ES-FEM model, the gradient of the acoustic pressure (the acoustic particle velocity) is smoothed and the numerical integration is implemented using Greens theorem and Gauss integration, then the discretized linear system equations are established using smoothed Galerkin weak form with smoothing domains associated with the edges of the triangular elements. Due to the proper softening effect provided by the edge-based gradient smoothing operation, a close-to-exact stiffness of the system can be obtained, and then the numerical dispersion error can be significantly decreased. In order to handle the underwater acoustic scattering problems in an infinite domain, the unbounded domain is truncated by an artificial boundary on which the well-known Dirichlet-to-Neumann (DtN) boundary condition is imposed to replace the Sommerfeld condition at infinity in this paper. Several numerical examples are investigated and the results show that the ES-FEM can achieve more accutate solutions compared to the standard FEM.