Narrow Results

The scalar wave equation in a two-dimensional semi-infinite wave guide is considered. The recently proposed Hagstrom–Warburton (H–W) local high-order absorbing boundary conditions (ABCs), which are based on a modification of the Higdon ABCs, are presented in this context. The P-order ABC involves the free parameters 0 < a_j ≤ 1, for j = 0, 1, …, P, which have to be chosen. The choice a_j = 1 for all j is shown to be satisfactory, in general, although not necessarily optimal. The optimal choice of the parameters is discussed via both theoretical analysis and numerical experiments. In addition, an adaptive scheme which controls the time-varying values of P and a_j is presented and tested.

A new high-order local Absorbing Boundary Condition (ABC) has been recently proposed for use on an artificial boundary for time-dependent elastic waves in unbounded domains, in two dimensions. It is based on the stress–velocity formulation of the elastodynamics problem, and on the general Complete Radiation Boundary Condition (CRBC) approach, originally devised by Hagstrom and Warburton in 2009. The work presented here is a sequel to previous work that concentrated on the stability of the scheme; this is the first known high-order ABC for elastodynamics which is long-time stable. Stability was established both theoretically and numerically. The present paper focuses on the accuracy of the scheme. In particular, two accuracy-related issues are investigated. First, the reflection coefficients associated with the new CRBC for different types of incident and reflected elastic waves are analyzed. Second, various choices of computational parameters for the CRBC, and their effect on the accuracy, are discussed. These choices include the optimal coefficients proposed by Hagstrom and Warburton for the acoustic case, and a simplified formula for these coefficients. A finite difference discretization is employed in space and time. Numerical examples are used to experiment with the scheme and demonstrate the above-mentioned accuracy issues.

In order to study the influence of pile-soil-structure dynamic interaction caused by seismic activity on long-span cable-stayed bridges, a seismic analysis is carried out using the JiangShun bridge, which has a main span of 700m. The key dynamic parameters of the concentrated mass model are given by the M method, viscoelastic artificial boundary method and radiation damping theory. The numerical model is established by Midas/Civil, and the dynamic interaction influence law on cable-stayed bridge is analyzed. The results show that regardless of the earthquake's action being vertical or horizontal, the pile internal force response of the concentrated mass model remains the smallest among the three model types. Moreover, the pile top force response value is 30% smaller than that from the engineering simplified model. This is mainly due to radiation damping which results from the scattering of seismic waves into the infinite foundation through wave propagation.