Modelling the transient interaction of a thin elastic shell with an exterior acoustic field

Chappell, David J.; Harris, Paul J.; Henwood, David; Chakrabarti, R.

doi:10.1002/nme.2253

Cited by 10 publications

(7 citation statements)

References 19 publications

(56 reference statements)

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“…The dynamics of a coupled vibro-acoustic system, spatially discretized using the FE method, are described by the set of ordinary differential equations MR x C CP x C Kx D F; (1) where M, C and K 2 C n n are the mass, damping and stiffness matrices and F 2 C n is the forcing vector. The total number of DOFs is denoted as n and is the sum of the total number of structural DOFs n s and acoustic DOFs n a .…”

Section: Finite Element Modelling Of Coupled Vibro-acoustic Systemsmentioning

confidence: 99%

“…To overcome this problem, one can turn to MOR techniques to reduce the system size while still retaining a high level of accuracy. In projection-based MOR for systems described by (1), one attempts to find a left projection matrix W 2 C n r and a right projection matrix V 2 C n r such that the projected system…”

Section: Projection-based Mor For Vibro-acoustic Fe Modelsmentioning

confidence: 99%

“…Conventional simulation methods analyze (vibro-)acoustic problems in the frequency-domain, but transient analysis in the time-domain is important to assess the product sound quality. This is why transient simulation techniques have received an increasing amount of attention in recent literature [1][2][3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

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Stability‐preserving model order reduction for time‐domain simulation of vibro‐acoustic FE models

Walle

Naets

Deckers

et al. 2016

Numerical Meth Engineering

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This work proposes novel stability-preserving model order reduction approaches for vibro-acoustic finite element models. As most research in the past for these systems has focused on noise attenuation in the frequency-domain, stability-preserving properties were of low priority. However, as the interest for timedomain auralization and (model based) active noise control increases, stability-preserving model order reduction techniques are becoming indispensable. The original finite element models for vibro-acoustic simulation are already well established but require too much computational load for these applications. This work therefore proposes two new global approaches for the generation of stable reduced-order models. Based on proven conditions for stability preservation under one-sided projection, a reformulation of the displacement-fluid velocity potential (u ) formulation is proposed. In contrast to the regular formulation, the proposed approach leads to a new asymmetric structure for the system matrices which is proven to preserve stability under one-sided projection. The second approach starts from a displacement-pressure (u p) description where the system level projection space is decoupled for the two domains, for which we also prove the preservation of stability. Two numerical validation cases are presented which demonstrate the inadequacy of straightforward model order reduction on typical vibro-acoustic models for time-domain simulation and compare the performance of the proposed approaches. Both proposed approaches effectively preserve the stability of the original system. formulation is that it results in a real dynamic stiffness matrix for undamped frequency-domain simulations and in a real eigenvalue problem for the computation of the undamped modes. It is the standard formulation used in most commercial FE tools for coupled vibro-acoustic analysis [10].One of the major drawbacks of element-based methods is their computational cost, which scales unfavourably with increasing problem size and frequency, restricting the overall practical applicability. In order to accurately describe the wave-like spatial character of the variables, the use of locally defined and low-order shape functions imposes minimum requirements on the number of elements used per wavelength and therefore limits the maximum element size for a given wavelength [11]. The highest frequency of interest determines the smallest wavelength present in the model, which in turn dictates the maximum element size. Because of the three-dimensional nature of acoustics, the number of elements in the model grows rapidly with increasing problem size or equivalently with decreasing element size (and thus also with increasing frequency). In order to alleviate the problems associated with computational costs, one can turn to model order reduction (MOR) techniques to reduce the number of DOFs for a desired accuracy [12]. For coupled vibro-acoustic problems, the advantages of MOR have already been demonstrated in frequency-domain analysis [10,13,14]. I...

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Section: Finite Element Modelling Of Coupled Vibro-acoustic Systemsmentioning

confidence: 99%

Section: Projection-based Mor For Vibro-acoustic Fe Modelsmentioning

confidence: 99%

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Stability‐preserving model order reduction for time‐domain simulation of vibro‐acoustic FE models

Walle

Naets

Deckers

et al. 2016

Numerical Meth Engineering

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“…It also has the advantage that the inner integration over the rotational angle around the axis of symmetry for (74) and (75) may be performed analytically in terms of elliptic integrals (the outer ones are simply a multiplication by 2 ). The remaining integrals are carried out using a suitable numerical rule, including a tanh transformation for the weakly singular element as employed in [28]. The numerical integration over the generating curve (see Figure 2) becomes increasingly subdivided as the spatial mesh is refined, but this is not so far the numerical integration over the rotational angle.…”

Section: Corollary 52mentioning

confidence: 99%

A convolution quadrature Galerkin boundary element method for the exterior Neumann problem of the wave equation

Chappell

2009

Math Methods in App Sciences

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SUMMARYThe numerical solution of the Neumann problem of the wave equation on unbounded three-dimensional domains is calculated using the convolution quadrature method for the time discretization and a Galerkin boundary element method for the spatial discretization. The mathematical analysis that has been built up for the Dirichlet problem is extended and developed for the Neumann problem, which is important for many modelling applications. Numerical examples are then presented for one of these applications, modelling transient acoustic radiation.

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“…Bhattacharyya and Premkumar [10] formulated non-reverberating surface conditions in spheroidal coordinates for non-stationary structure/fluid coupling analysis of immersed spheroidal bodies including that of a spherical shell. Chappell et al [11] used a coupled time domain finite and boundary element technique to characterize the non-stationary sound radiation by a thin elastic spherical shell. Lee et al [12] employed a weighted combination of the delayed and progressive potentials for external acoustic interaction analysis of submerged thin flexible spherical shells.…”

Section: Introductionmentioning

confidence: 99%

Transient acoustic radiation from an eccentric sphere

Hasheminejad

Mousavi-Akbarzadeh

2015

Applied Mathematical Modelling

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a b s t r a c tA vigorous semi-analytical model is offered to describe the 3D coupled nonaxisymmetric non-steady acousto-elastodynamic behavior of a submerged solid sphere with an off-center fluid-filled spherical cavity, acted upon by general distributed time-varying mechanical loads at its internal and/or external boundaries. The solid medium is designated by the 3D Navier's linear elasticity model, while the internal/external ideal compressible fluids are assumed to obey the classical linear acoustic theory. Laplace transformation is applied to the time variable, and the separation of variables technique together with the pertinent fluid/solid interface conditions, the classical orthogonality properties of spherical harmonics, and a modified form of the translational addition theorem for spherical vector wave functions, are utilized to attain the final matrix equations in terms of unknown modal coefficients. Durbin's Laplace transform inversion algorithm is subsequently applied to compute the pressure/displacement time response histories of water-submerged eccentric and coaxial metallic spheres excited by a couple of external concentrated Ricker-pulse radial excitations. Also, some key characteristics of the transient structure/liquid interaction phenomena with respect to cavity eccentricity are noted based on selected two-dimensional visualizations of the internal/external sound fields. Lastly, the accuracy of numerical simulations is verified by employing a standard FEM software.

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Modelling the transient interaction of a thin elastic shell with an exterior acoustic field

Cited by 10 publications

References 19 publications

Stability‐preserving model order reduction for time‐domain simulation of vibro‐acoustic FE models

Stability‐preserving model order reduction for time‐domain simulation of vibro‐acoustic FE models

A convolution quadrature Galerkin boundary element method for the exterior Neumann problem of the wave equation

Transient acoustic radiation from an eccentric sphere

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