Consistent transmitting boundary conditions with a reduced number of eigenmodes for wave propagation in elastic media

Hamdan, Nawras; Laghrouche, Omar; Kacimi, A. El; Woodward, Peter Keith

doi:10.1016/j.compgeo.2013.04.006

Cited by 6 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where U is a matrix composed of eigenvectors, K 2 is the eigenvalue matrix of diagonal form. Mode reduction (Hamdan et al, 2013;Kim et al, 2017) is introduced, and the following equations can be obtained as:…”

Section: Semi-discrete Finite Element Equation In the Modal Spacementioning

confidence: 99%

A high-order absorbing boundary condition for scalar wave propagation simulation in viscoelastic multilayered medium

Zhao

2020

View full text Add to dashboard Cite

Purpose The finite element method (FEM) is used to calculate the two-dimensional anti-plane dynamic response of structure embedded in D’Alembert viscoelastic multilayered soil on the rigid bedrock. This paper aims to research a time-domain absorbing boundary condition (ABC), which should be imposed on the truncation boundary of the finite domain to represent the dynamic interaction between the truncated infinite domain and the finite domain. Design/methodology/approach A high-order ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. A new operator separation method and the mode reduction are adopted to construct the time-domain ABC. Findings The derivation of the ABC is accurate for the single layer but less accurate for the multilayer. To achieve high accuracy, therefore, the distance from the truncation boundary to the region of interest can be zero for the single layer but need to be about 0.5 times of the total layer height of the infinite domain for the multilayer. Both single-layered and multilayered numerical examples verify that the accuracy of the ABC is almost the same for both cases of only using the modal number excited by dynamic load and using the full modal number of infinite domain. Using the ABC with reduced modes can not only reduce the computation cost but also be more friendly to the stability. Numerical examples demonstrate the superior properties of the proposed ABC with stability, high accuracy and remarkable coupling with the FEM. Originality/value A high-order time-domain ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. The proposed ABC is suitable for both linear elastic and D’Alembert viscoelastic media, and it can be coupled seamlessly with the FEM. A new operator separation method combining mode reduction is presented with better stability than the existing methods.

show abstract

Section: Semi-discrete Finite Element Equation In the Modal Spacementioning

confidence: 99%

A high-order absorbing boundary condition for scalar wave propagation simulation in viscoelastic multilayered medium

Zhao

2020

View full text Add to dashboard Cite

show abstract

“…The same example examined by Park and Tassoulas (2002) and Hamdan et al (2013) is revisited here. The foundation has a width of 2B, where 2B = H, with H being the thickness of the soil layer.…”

Section: 1mentioning

confidence: 99%

“…This yields to an eigenvalue problem with 2n eigenvalues and corresponding eigenvectors. Hamdan et al (2013) investigated the effect of selecting a few eigenmodes and hence reducing the computational cost of the method. Kausel and Roësset (1981) derived an exact form for the dynamic impedance matrix for SV-P waves in a half-space.…”

Section: Methods Of Analysismentioning

confidence: 99%

“…The soil medium has shear modulus and density of unit values, a Poisson ratio of 0·3 and a damping coefficient of 0·05. The bedrock is assumed to be horizontal in the first instance, θ = 0°, in order to obtain a reference solution and for which the analytical solution, Kramer (1996), and numerical solutions, Park and Tassoulas (2002) and Hamdan et al (2013), are available. The problem is illustrated in Figure 2(a) where the surface rigid foundation is resting on a soil layer over an inclined rigid base.…”

Section: 1mentioning

confidence: 99%

“…The TLM was first developed by Waas (1972) and has been extended and used by various other authors such as Kausel (1974), Tassoulas (1981), Laghrouche (1996), Park and Tassoulas (2002), Ikeda and Tassoulas (2008), Hamdan et al (2013) and others. It can be used to compute the nodal forces needed on the lateral domain boundaries to allow wave radiation to infinity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling ground vibrations induced by harmonic loads

Hamdan

Laghrouche

Connolly

et al. 2016

Proceedings of the Institution of Civil Engineers - Geotechnica

View full text Add to dashboard Cite

2 3 4A finite-element model combining the frequency domain thin-layer method with paraxial boundary conditions to simulate the semi-infinite extent of a soil medium is presented in this paper. The combined numerical model is used to deal with harmonic vibrations of surface rigid foundations on non-horizontal soil profiles. The model can deal with soil media over rigid bedrock or significant depths of half-space. Structured finite elements are used to mesh simple geometry soil domains, whereas unstructured triangular mesh grids are employed to deal with complex geometry problems. Dynamic responses of homogeneous as well as layered soil profiles are simulated and validated against analytical and approximate solutions. Finally, the model is used to deal with surface ground vibration reduction, in which it is first validated against published results and then followed by an example involving a bridge.

show abstract

Stable high-order absorbing boundary condition based on new continued fraction for scalar wave propagation in unbounded multilayer media

Zhao

et al. 2018

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Consistent transmitting boundary conditions with a reduced number of eigenmodes for wave propagation in elastic media

Cited by 6 publications

References 12 publications

A high-order absorbing boundary condition for scalar wave propagation simulation in viscoelastic multilayered medium

A high-order absorbing boundary condition for scalar wave propagation simulation in viscoelastic multilayered medium

Modelling ground vibrations induced by harmonic loads

Stable high-order absorbing boundary condition based on new continued fraction for scalar wave propagation in unbounded multilayer media

Contact Info

Product

Resources

About