Numerical evaluation of the damping‐solvent extraction method in the frequency domain

Abstract

SUMMARYThe damping-solvent extraction method for the analysis of unbounded visco-elastic media is evaluated numerically in the frequency domain in order to investigate the in uence of the computational parameters -domain size, amount of artiÿcial damping, and mesh density -on the accuracy of results. An analytical estimate of this in uence is presented, and speciÿc questions regarding the in uence of the parameters on the results are answered using the analytical estimate and numerical results for two classical problems: the rigid strip and rigid disc footings on a visco-elastic half-space with constant hysteretic material damping.As the domain size in increased, the results become more accurate only at lower frequencies, but are essentially una ected at higher frequencies. Choosing the domain size to ensure that the static sti ness is computed accurately leads to an unnecessarily large domain for analysis at higher frequencies. The results improve by increasing artiÿcial damping but at a slower rate as the total (material plus artiÿcial) damping ratio t gets closer to 0.866. However, the results do not deteriorate signiÿcantly for the larger amounts of artiÿcial damping, suggesting that t ≈ 0:6 is appropriate; a larger value is not likely to in uence the accuracy of results. Presented results do not support the earlier suggestion that similar accuracy can be achieved by a large bounded domain with small damping or by a small domain with larger damping.

An efficient time‐domain damping solvent extraction algorithm and its application to arch dam–foundation interaction analysis

“…It implies that if any computational errors exist in evaluating {u b }, {u b } and {ü b }, then the errors in {u rb }, {u rb } and {ü rb } are enlarged with a weighing factor increasing with time t. As a result, the error evaluating {R r (t)} is accumulated with time since {R r (t)} is an expression with the time parameter t explicitly included, which could be seen easily by substituting Equations (9) into the lower part of Equation (8). What is more, this may cause difficulty in convergence of the algorithm.…”

Complex Frequencies in Elastodynamics, with Application to the Damping-Solvent Extraction Method

“…small changes in damping). In those cases the derivatives with respect to frequency can be estimated numerically by differentiation, or even obtained with modest additional computational effort directly and simultaneously with the response, as was done by Basu and Chopra (2002).…”

“…As a counter-example to the previous, very well-behaved problem, consider next a rod of finite length 1 L that is followed by another rod of infinite length 2 L   and different material properties. The goal here is to assess the DSE for a heterogeneous medium where waves may reverberate within the system even when the medium is infinitely long.…”

“…In addition, the original theoretical formulation of the DSE was lacking in rigor, and the empirical proof of concept resorted to models containing numerous confounding effects, such as discretization errors, elastic foundations, absorbing boundaries, or material damping, all of which made general assessments and predictions difficult. This situation led Basu and Chopra (2002) to carry out a lengthy assessment of this method in which they attempted to pin down some of the missing characteristics, but they attained only mixed results that still left many unanswered questions. For this reason, we take up this subject here again and explore the use of complex frequencies in the context of the DSE by means of exact, yet simple canonical models that provide greater transparency into the effects of the various parameters.…”

On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

“…Soil-Structure Interaction (SSI) is a typical civil engineering problem [1][2][3][4][5][6][7][8][9]. The infinite elements can be integrated in the Finite element method codes [10][11][12] adequately, and then dynamic SSI simulations can be obtained.…”