Vibrations of Flexible Strip on Viscoelastic Halfspace

Abstract

The dynamic response of rigid and flexible foundations on the soil has been subject of extensive study in the past decades. A hybrid method using a combined finite element method (FEM) and boundary element method (BEM) is the most common method used for solving this problem. The objective of this paper is to present an effective frequency domain method to obtain the dynamic response of a flexible strip foundation resting on a viscoelastic halfspace. The foundation is treated with the spectral element method (SEM), while the soil is modelled using the integral transform method (ITM). Both SEM and ITM are based on the analytical solution of the Lame-equations in the frequency domain and therefore are suitable for combining. The solution is obtained in the transformed space-frequency or wavenumber-frequency domain using the Fourier transformation. The study is performed as a 2D plane-strain analysis, assuming that the foundation cross-section behaves as an Euler-Bernoulli beam and that there is no sliding between the foundation and the soil, nor discontinuities in terms of the displacement field. The vertical displacements field of the foundation is described by a set of modal functions corresponding to free vibration mode shapes of a SEM Euler-Bernoulli beam element. The coupling between the foundation and the soil is achieved using the modal soil impedance functions, which are determined by using the ITM. The displacements of the coupled foundation-soil system are solved by the modal superposition method. The accuracy of the proposed method is assessed by comparing the obtained results with the results obtained by a commercial software package SASSI2000. The comparison shows that the presented method is accurate and less costly in terms of computational effort, especially in the high frequency range. The presented method can be easily extended to provide the solution of the response of a flexible strip on a layered halfspace due to a horizontal and vertical excitation.