Implementation of the nodal discontinuous Galerkin method for the plate vibration problem using linear elasticity equations

Research output: Contribution to journalArticleAcademicpeer-review

2 Downloads (Pure)

Abstract

This work presents a numerical solution of the forced plate vibration problem using the nodal discontinuous Galerkin (DG) method. The plate is modelled as a three-dimensional domain, and its vibration is governed by the linear elasticity equations. The nodal DG method discretises the spatial domain and computes the spatial derivatives of the equations element-wise, while the time integration is conducted using the Runge-Kutta method. This method is in particular of interest as it is very favourable to carry out the computation by a parallel implementation. Several aspects regarding the numerical implementation such as the plate boundary conditions, the point force excitation, and the upwind numerical flux are presented. The numerical results are validated for rectangular concrete plates with different sets of boundary conditions and thicknesses, by a comparison with the exact mobilities that are derived from the classical plate theory (CPT) and the first order shear deformation theory (FSDT). The plate thickness is varied to understand its effect regarding the comparison with the CPT. An excellent agreement between the numerical solution and the FSDT was found. The agreement with the CPT occurs only at the first couple of resonance frequencies, and as the plate is getting thinner. Furthermore, the numerical example is extended to an L-shaped concrete plate. The mobility is then compared with the mobilities obtained by the CPT, FSDT, and linear elasticity equations.

Original languageEnglish
Pages (from-to)668-681
Number of pages14
JournalActa Acustica united with Acustica
Volume105
Issue number4
DOIs
Publication statusPublished - 1 Jul 2019

Fingerprint

Galerkin method
elastic properties
plate theory
vibration
shear
boundary conditions
Runge-Kutta method
Elasticity
Equations
excitation

Cite this

@article{bc29c98d3e3f48438db715fd748fc757,
title = "Implementation of the nodal discontinuous Galerkin method for the plate vibration problem using linear elasticity equations",
abstract = "This work presents a numerical solution of the forced plate vibration problem using the nodal discontinuous Galerkin (DG) method. The plate is modelled as a three-dimensional domain, and its vibration is governed by the linear elasticity equations. The nodal DG method discretises the spatial domain and computes the spatial derivatives of the equations element-wise, while the time integration is conducted using the Runge-Kutta method. This method is in particular of interest as it is very favourable to carry out the computation by a parallel implementation. Several aspects regarding the numerical implementation such as the plate boundary conditions, the point force excitation, and the upwind numerical flux are presented. The numerical results are validated for rectangular concrete plates with different sets of boundary conditions and thicknesses, by a comparison with the exact mobilities that are derived from the classical plate theory (CPT) and the first order shear deformation theory (FSDT). The plate thickness is varied to understand its effect regarding the comparison with the CPT. An excellent agreement between the numerical solution and the FSDT was found. The agreement with the CPT occurs only at the first couple of resonance frequencies, and as the plate is getting thinner. Furthermore, the numerical example is extended to an L-shaped concrete plate. The mobility is then compared with the mobilities obtained by the CPT, FSDT, and linear elasticity equations.",
author = "Indra Sihar and Maarten Hornikx",
year = "2019",
month = "7",
day = "1",
doi = "10.3813/AAA.919347",
language = "English",
volume = "105",
pages = "668--681",
journal = "Acta Acustica united with Acustica",
issn = "1610-1928",
publisher = "S. Hirzel Verlag GmbH",
number = "4",

}

Implementation of the nodal discontinuous Galerkin method for the plate vibration problem using linear elasticity equations. / Sihar, Indra; Hornikx, Maarten.

In: Acta Acustica united with Acustica, Vol. 105, No. 4, 01.07.2019, p. 668-681.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Implementation of the nodal discontinuous Galerkin method for the plate vibration problem using linear elasticity equations

AU - Sihar, Indra

AU - Hornikx, Maarten

PY - 2019/7/1

Y1 - 2019/7/1

N2 - This work presents a numerical solution of the forced plate vibration problem using the nodal discontinuous Galerkin (DG) method. The plate is modelled as a three-dimensional domain, and its vibration is governed by the linear elasticity equations. The nodal DG method discretises the spatial domain and computes the spatial derivatives of the equations element-wise, while the time integration is conducted using the Runge-Kutta method. This method is in particular of interest as it is very favourable to carry out the computation by a parallel implementation. Several aspects regarding the numerical implementation such as the plate boundary conditions, the point force excitation, and the upwind numerical flux are presented. The numerical results are validated for rectangular concrete plates with different sets of boundary conditions and thicknesses, by a comparison with the exact mobilities that are derived from the classical plate theory (CPT) and the first order shear deformation theory (FSDT). The plate thickness is varied to understand its effect regarding the comparison with the CPT. An excellent agreement between the numerical solution and the FSDT was found. The agreement with the CPT occurs only at the first couple of resonance frequencies, and as the plate is getting thinner. Furthermore, the numerical example is extended to an L-shaped concrete plate. The mobility is then compared with the mobilities obtained by the CPT, FSDT, and linear elasticity equations.

AB - This work presents a numerical solution of the forced plate vibration problem using the nodal discontinuous Galerkin (DG) method. The plate is modelled as a three-dimensional domain, and its vibration is governed by the linear elasticity equations. The nodal DG method discretises the spatial domain and computes the spatial derivatives of the equations element-wise, while the time integration is conducted using the Runge-Kutta method. This method is in particular of interest as it is very favourable to carry out the computation by a parallel implementation. Several aspects regarding the numerical implementation such as the plate boundary conditions, the point force excitation, and the upwind numerical flux are presented. The numerical results are validated for rectangular concrete plates with different sets of boundary conditions and thicknesses, by a comparison with the exact mobilities that are derived from the classical plate theory (CPT) and the first order shear deformation theory (FSDT). The plate thickness is varied to understand its effect regarding the comparison with the CPT. An excellent agreement between the numerical solution and the FSDT was found. The agreement with the CPT occurs only at the first couple of resonance frequencies, and as the plate is getting thinner. Furthermore, the numerical example is extended to an L-shaped concrete plate. The mobility is then compared with the mobilities obtained by the CPT, FSDT, and linear elasticity equations.

UR - http://www.scopus.com/inward/record.url?scp=85075265423&partnerID=8YFLogxK

U2 - 10.3813/AAA.919347

DO - 10.3813/AAA.919347

M3 - Article

AN - SCOPUS:85075265423

VL - 105

SP - 668

EP - 681

JO - Acta Acustica united with Acustica

JF - Acta Acustica united with Acustica

SN - 1610-1928

IS - 4

ER -