Abstract
Conventional finite element method (FEM) is capable of obtaining wave solutions, but large discretized structures at high frequency require high computational resources, the computational domain can be reduced by combining FEM with analytical assumption for guided wave. Semi Analytical Finite Element (SAFE) formulation for immersed waveguide in perfect fluid is used for acquiring propagating wave modes as dynamic equilibrium states. Modes are solutions to eigenvalue problem and provide with important characteristic features of the guided waves – phase velocity, attenuation, wave structure, etc. The effect of surrounding leaky medium is modeled via traction boundary condition, which is based on assumption of the continuity of stresses at solid-fluid interface. The boundary condition causes wave attenuation due to energy leakage into outer medium. The derivation of the eigen-problem takes into account complex wavenumbers of leaky wave in fluid and guided wave in a three-dimensional waveguide. Linearization procedure for solving nonlinear eigenvalue problem is used. Dispersion relations for immersed waveguide with Rayleigh damping are obtained. The limits of applications of Rayleigh damping and convergence analysis of immersed waveguide model are discussed.
Highlights
Periodic loading on the structure causes its dynamic response as an elastic wave
Guided waves can be widely applied in various fields such as non-destructive testing (NDT) [3]
The 2.5 D boundary element technique was used to model the surrounding leaky medium. This approach involves complex non-linear eigen problem for obtaining wavenumbers for damped waveguide, computational time for this technique is greater in comparison to Semi Analytical Finite Element (SAFE) formulation coupled to infinite element or perfectly matched layer (PML) [14]
Summary
Periodic loading on the structure causes its dynamic response as an elastic wave. Guided waves can be widely applied in various fields such as non-destructive testing (NDT) [3]. The problems including concrete rods buried in soil or thin walled pipes (hollow cylinders) filled with fluid require modeling the surrounding leaky medium, which causes propagating wave to attenuate due to leakage of the energy. The 2.5 D boundary element technique was used to model the surrounding leaky medium This approach involves complex non-linear eigen problem for obtaining wavenumbers for damped waveguide, computational time for this technique is greater in comparison to SAFE formulation coupled to infinite element or PML [14]. An iterative exact dashpot boundary condition was employed in SBFEM for obtaining the wavenumbers for waveguide immersed in perfect fluid [7], Hayashi et al has extended SAFE formulation for plates loaded with leaky medium [11]. The theoretical investigation of the impact of Rayleigh damping to dispersion relations for immersed waveguide is carried out
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