A stochastic perturbation edge-based smoothed finite element method for the analysis of uncertain structural-acoustics problems with random variables

Wu, Fengqin; Yao, Lingyun; Hu, M.; He, Z.C.

doi:10.1016/j.enganabound.2017.03.008

Cited by 27 publications

(3 citation statements)

References 32 publications

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“…By imposing the TBC on the boundary of the truncated domain, the reflection of the wave can be avoided. The TBC has been used for solving many wave scattering problems [17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

Yue¹,

Wang²,

Li³

2023

AAMM

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In this paper, a node-based smoothed finite element method (NS-FEM) with linear gradient fields (NS-FEM-L) is presented to solve elastic wave scattering by a rigid obstacle. By using Helmholtz decomposition, the problem is transformed into a boundary value problem with coupled boundary conditions. In numerical analysis, the perfectly matched layer (PML) and transparent boundary condition (TBC) are introduced to truncate the unbounded domain. Then, a linear gradient is constructed in a node-based smoothing domain (N-SD) by using a complete order of polynomial. The unknown coefficients of the smoothed linear gradient function can be solved by three linearly independent weight functions. Further, based on the weakened weak formulation, a system of linear equation with the smoothed gradient is established for NS-FEM-L with PML or TBC. Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy. It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness matrix, which effectively overcomes the instability of original NS-FEM. Moreover, the convergence rates of L 2 and H 1 semi-norm errors for the two NS-FEM-L models are also higher.

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Section: Introductionmentioning

confidence: 99%

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

Yue¹,

Wang²,

Li³

2023

AAMM

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“…Here, the traditional stochastic method has been one of the most common methods to deal with uncertainty response analysis in engineering applications on the basis of probability theory. For example, a novel stochastic perturbation method is proposed for the analysis of structural-acoustic problems combined with the edge-based smoothed finite element method (Wu et al, 2017). The polynomial chaos expansion procedure based on the sparse grid collocation strategy is used to handle the random uncertainty for structural-acoustic systems with hybrid uncertainties (Xu et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Statistical energy analysis for vibro-acoustic coupled system with fuzzy parameters

Wang

Wu²,

Wang³

et al. 2018

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Purpose This paper aims to propose a novel statistic energy analysis method with fuzzy parameters to study the dynamic and acoustic responses of coupled system with fuzzy parameters, which can expand the applied range of statistic energy analysis method in engineering to some extent. Design/methodology/approach On the basis of the property of membership level, the uncertain fuzzy parameters are expressed as the interval forms. Interval mathematics and interval expansion principle are adopted to solve the problem with interval parameters. At last, two numerical examples, which include a two-plate coupled system and a single-partition sound-insulation system, are carried out to demonstrate the feasibility and validity of the presented method. Findings Interval mathematics and interval expansion principle are adopted to solve the problem with interval parameters. Originality/value By integrating the interval analysis, optimization technique and Taylor expansion method, two non-probabilistic, set-theoretical statistical energy analyses are proposed for predicting the dynamical and acoustical response of the complex coupled system with uncertain parameters in high-frequency domain.

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“…Moreover, CS-FEM does not require the shape function derivatives or high generosity of program and is insensitive to mesh distortion because of the absence of isoparametric mapping. CS-FEM has been successfully extended into dynamical control of piezoelectric sensors and actuators, topological optimization of linear piezoelectric micromotor, and analysis of static behaviors, frequency, and defects of piezoelectric structures [33][34][35][36][37][38][39][40][41][42][43]. Due to its versatility, CS-FEM becomes a simple and effective numerical tool to solve numerous electric and mechanical physical problems.…”

Section: Introductionmentioning

confidence: 99%

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

Cai

Meng

Wang

2018

Shock and Vibration

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To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

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A stochastic perturbation edge-based smoothed finite element method for the analysis of uncertain structural-acoustics problems with random variables

Cited by 27 publications

References 32 publications

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

Statistical energy analysis for vibro-acoustic coupled system with fuzzy parameters

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

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