FFT-based spectral analysis methodology for one-dimensional wave propagation in poroelastic media

The general one-dimensional equilibrium equations describing the dynamic behaviour of a porous medium form a system of coupled hyperbolic partial differential equations. A transition from the time to the frequency domain is made by spectral decomposition of the displacements. The equations simplify to a set of coupled ordinary differential equations. A solution can be obtained by solving a frequency-dependent eigenvalue problem. The characteristic equation clarifies the double wave-pattern and the attenuation of each wave. A spectrally formulated element uses the frequency-dependent eivenvectors as shape functions. The mass distribution is treated exactly without the need of subdividing a member into smaller elements and therefore wave propagation within an element is also treated exactly.