Modeling of axisymmetric wave modes in a poroelastic cylinder using spectral method

Abstract

Algorithm and code are presented which solve the dispersion equation for cylindrical poroelastic structures. The algorithm is based on the spectral method, which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. The results are illustrated for the case of a fluid-saturated free cylinder with open- and closed-pore boundary conditions on its surface. The computed dispersion curves are in good agreement with analytical results, which confirms the accuracy of the method.

Tube wave signatures in cylindrically layered poroelastic media computed with spectral method

“…The have to be individually discretized for each poroelastic layer using Chebyshev points as well as differentiation matrices. For the case of a free poroelastic cylinder, the dispersion of the axisymmetric modes has been presented by Karpfinger et al (2008b). In this paper we extend this approach for an arbitrary number of fluid, elastic and poroelastic layers.…”

“…The pore pressure condition is replaced by the condition that relative motion of fluid with respect to solid is zero on the surface of the cylinder. For a single poroelastic cylinder these boundary conditions are discussed by Berryman (1983) and Karpfinger et al (2008b).…”

Modeling guided elastic waves in generally anisotropic media using a spectral collocation method

“…Karpfinger et al, [21], have successfully used this method to handle multi-layered cylindrical systems with isotropic materials and later [37] extended this to porous elastic media and to geophysical applications involving boreholes [38]. Yu et al, [23], used the spectral method, combined with root finding routines, for multi-layered isotropic cylinders with axial propagation and weak and perfect interfaces.…”

Guided waves' dispersion curves in anisotropic viscoelastic single- and multi-layered media

“…As pointed out in [22], spectral methods were introduced in the 1970s in the field of fluid dynamics by Kreiss & Oliger [23], Orszag [24] and Fornberg [25] and have remained a standard computational tool in the field ever since. Recently, the SCM has been successfully used in the fields of seismology and geophysics to study wave propagation, see for instance [26][27][28]. Guided wave problems in other contexts such as electromagnetic waveguides can also be tackled by means of the SCM, see for instance [29], where metal-insulator-metal electromagnetic lossless and lossy waveguides are studied.…”