Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

Jog, C. S.; Nandy, Arup

doi:10.1115/1.4029075

Cited by 16 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is difficult to directly study the stability of a second-order system as in (1) or its reduced-order counterpart in (7). We therefore introduce the concept of a linear descriptor system because criteria 893 for stability are well established for this kind of system.…”

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

confidence: 99%

See 1 more Smart Citation

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

Walle

Naets

Deckers

et al. 2016

Numerical Meth Engineering

View full text Add to dashboard Cite

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...

show abstract

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%

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

Walle

Naets

Deckers

et al. 2016

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…The key notion is the choice and evaluation of stress interpolation functions which is inspired from the work of Jog [29,30] in context of conventional FEA framework. The efficient FE implementation of the stated approach for large-deformation contact mechanics [2], structural acoustics [32], electromagnetic analysis [31], analysis of electromechanical systems [1], and coupled fluid-structure problem [38] confirms the effectiveness and robustness of the method. In the present study, the systematic evaluation of stress interpolation functions specific to the NURBS interpolations and its effective implementation in a two-dimensional linear elasticity regime is investigated.…”

Section: Introductionmentioning

confidence: 86%

A novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

Bombarde¹,

Gautam²,

Nandy³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

In the present work, a novel class of hybrid elements is proposed to alleviate the locking anomaly in non-uniform rational B-spline (NURBS)-based isogeometric analysis (IGA) using a two-field Hellinger-Reissner variational principle. The proposed hybrid elements are derived by adopting the independent interpolation schemes for displacement and stress field. The key highlight of the present study is the choice and evaluation of higher-order terms for the stress interpolation function to provide a locking-free solution. Furthermore, the present study demonstrates the efficacy of the proposed elements with the treatment of several two-dimensional linear-elastic benchmark problems alongside the conventional single-field IGA, Lagrangian-based finite element analysis (FEA), and hybrid FEA formulation. It is shown that the proposed class of hybrid elements performs effectively for analyzing the nearly incompressible problem domains that are severely affected by volumetric locking along with the thin plate and shell problems where the shear and membrane locking is dominant. A better coarse mesh accuracy of the proposed method in comparison with the conventional formulation is demonstrated through various numerical examples. Moreover, the formulation is not restricted to the locking-dominated problem domains but can also be implemented to solve the problems of general form without any special treatment. Thus, the proposed method is robust, most efficient, and highly effective against different types of locking.

show abstract

“…A classical approach [29,30] to discretize in time the system of second-order differential equations (18) consists first in rewriting the system as a system of first-order differential equations by introducing the vector of velocities W = Q, i.e.…”

Section: Discrete Formulationmentioning

confidence: 99%

“…Regarding the discretization in time, several integration schemes have been adapted to linear elastodynamics [26,27,28]. Only stable, energy conservative discretization schemes are considered here, namely the Crank-Nicolson method [29,30,31] (also known as the implicit trapezoidal rule), and the Newmark method [32] with γ = 1/2 and β = 1/4. Moreover, we apply two post-processing procedures that aim at improving the convergence of the Galerkin-based version of the PGD [4,33], namely 1) the orthogonalization of the spatial modes via a modified Gram-Schmidt algorithm, and 2) the update procedure of the temporal modes.…”

Section: Introductionmentioning

confidence: 99%

PGD reduced-order modeling for structural dynamics applications

Vella¹,

Prudhomme²

2022

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Conservation Properties of the Trapezoidal Rule in Linear Time Domain Analysis of Acoustics and Structures

Cited by 16 publications

References 14 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 novel hybrid isogeometric element based on two-field Hellinger-Reissner principle to alleviate different types of locking

PGD reduced-order modeling for structural dynamics applications

Contact Info

Product

Resources

About