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The problems of acoustic waves scattered by scatterer immersed in unbounded domain is an essential ingredient in the study of acoustic-structure interaction. In this paper the problems of acoustic scattering in an infinite exterior region are investigated by using a fractal two-level finite element mesh with self-similar layers in the media which encloses the conventional finite element mesh for the cavity. The similarity ratio is bigger than one so that the fractal mesh extends to infinity. Because of the self-similarity, the equivalent stiffness (mass) matrix of one layer is proportional to the others. By means of the Hankel functions automatically satisfying Sommerfeld's radiation conditions at infinity, the different unknown nodal pressures on different layers are transformed to some common unknowns of the Hankel coefficients. The set of infinite number of unknowns of nodal pressure is reduced to the set of finite number of Hankel's coefficients. All layers have the same matrix dimension after the transformation and the respective matrices of each layer are summed. Due to the proportionality, the infinite number of layers can be summed in closed form as the entries of each matrix are in geometric series. That is, processing one layer is enough to virtually represent a set of infinite number of layers covering an infinity domain. No new elements are created. Numerical examples show that this method is efficient and accurate in solving unbounded acoustic problems.

The importance of soil–structure interaction analysis has been proven by many researchers. It is obvious that soil media should be considered as an infinite domain to represent the radiation of waves into infinity. Perfectly matched discrete layer (PMDL) is one of the most promising methods to describe properly the infinite domain in soil media in frequency and time domains. In this research, a modified version of PMDLs that has a different strategy to determine their parameters is proposed. The method is named perfectly matched discrete layers with analytical wavelengths (AW-PMDLs). For verification of the proposed method, the dynamic compliances of strip foundations are analyzed and validated in the frequency domain. In the analyses, frequency-dependent system properties and hysteretic (material) damping are considered. The results show that the proposed procedure, AW-PMDL method, is effective for soil–structure interaction analysis in the frequency domain.

Perfectly matched layer (PML) is known as one of the best methods to simulate infinite domains in many fields such as soil-structure interaction (SSI). The performance of PML is significantly affected by PML parameters selection. However, the way to select PML parameters still remains unclear. This study proposes a method for PML parameters determination for elastic wave propagation in two-dimensional (2D) media. The scaling and attenuation functions are developed in order to increase the accuracy and effectiveness of the PML. The proposed scheme is applied for a mixed PML in time domain. The finite element method (FEM) formulations of the PML are presented so that it can be easily applied to the existing codes. ABAQUS, a popular FEM code, is used for numerical applications in this study. The proposed PML is imported into ABAQUS by using a user-defined element (UEL) written in Fortran language. Six numerical analyses of SSI are implemented to prove the efficiency of the proposed PML. The numerical analyses cover many realistic problems, including free field, surface structure, and embedded structure problems. The results demonstrate the efficiency of the proposed PML in terms of the accuracy and computational cost.

It is known that the variable-order infinite acoustic wave envelope element (WEE) must be coupled with finite element method (FEM) by element matching for computing acoustic field radiated from radiators with complex geometric shapes. Therefore, the WEEs have to be reconstructed when the finite elements are refined or changed. To overcome the shortcoming, the element-free Galerkin (EFG) coupled with improved WEE (IWEE) method is presented to compute acoustic problems in the infinite domain. The continuity and compatibility of the acoustic pressure are maintained by IWEE that is composed of a standard WEE and a fictitious finite mesh. A key feature of the method is the introduction of the EFG method which is employed to eliminate the element matching and improve the accuracy of predicted acoustic pressure. The factors that affect the performance of the method are investigated by numerical examples, which include shape function construction, the weight function and the size of the influence domain. The numerical results show that the present method provides more accurate results compared to the coupled FEM-WEE method. The experimental results show that the method is very flexible for acoustic radiation prediction in the infinite domain.