LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS

C. M. Wang, W. X. Wu, C. Shu, T. Utsunomiya

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The Ritz method and some finite element formulations fail to furnish accurate modal stress-resultants for vibrating plates with free edges, even though the natural frequencies and mode shapes are accurately obtained. For example, by using the Ritz method, it was found that the modal twisting moments and shear forces violate the natural boundary conditions and that they contain erroneous "oscillations". This paper presents the least squares finite difference (LSFD) method for solving the freely vibrating plate problem. It will be shown herein that the modal stress-resultants obtained by the LSFD method satisfy the natural boundary conditions at the free edges without any oscillations.

Original languageEnglish
Pages (from-to)2329-2339
Number of pages11
JournalComputers and Structures
Volume84
Issue number31-32
DOIs
Publication statusPublished - Dec 1 2006
Externally publishedYes

Fingerprint

Ritz Method
Finite difference method
Difference Method
Least Squares
Finite Difference
Boundary conditions
Oscillation
Mode Shape
Violate
Natural Frequency
Natural frequencies
Finite Element
Moment
Formulation
Model

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Modelling and Simulation
  • Materials Science(all)
  • Mechanical Engineering
  • Computer Science Applications

Cite this

LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS. / Wang, C. M.; Wu, W. X.; Shu, C.; Utsunomiya, T.

In: Computers and Structures, Vol. 84, No. 31-32, 01.12.2006, p. 2329-2339.

Research output: Contribution to journalArticle

@article{45679a3efcaf473387bd2216fcc19daa,
title = "LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS",
abstract = "The Ritz method and some finite element formulations fail to furnish accurate modal stress-resultants for vibrating plates with free edges, even though the natural frequencies and mode shapes are accurately obtained. For example, by using the Ritz method, it was found that the modal twisting moments and shear forces violate the natural boundary conditions and that they contain erroneous {"}oscillations{"}. This paper presents the least squares finite difference (LSFD) method for solving the freely vibrating plate problem. It will be shown herein that the modal stress-resultants obtained by the LSFD method satisfy the natural boundary conditions at the free edges without any oscillations.",
author = "Wang, {C. M.} and Wu, {W. X.} and C. Shu and T. Utsunomiya",
year = "2006",
month = "12",
day = "1",
doi = "10.1016/j.compstruc.2006.08.055",
language = "English",
volume = "84",
pages = "2329--2339",
journal = "Computers and Structures",
issn = "0045-7949",
publisher = "Elsevier Limited",
number = "31-32",

}

TY - JOUR

T1 - LSFD method for accurate vibration modes and modal stress-resultants of freely vibrating plates that model VLFS

AU - Wang, C. M.

AU - Wu, W. X.

AU - Shu, C.

AU - Utsunomiya, T.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - The Ritz method and some finite element formulations fail to furnish accurate modal stress-resultants for vibrating plates with free edges, even though the natural frequencies and mode shapes are accurately obtained. For example, by using the Ritz method, it was found that the modal twisting moments and shear forces violate the natural boundary conditions and that they contain erroneous "oscillations". This paper presents the least squares finite difference (LSFD) method for solving the freely vibrating plate problem. It will be shown herein that the modal stress-resultants obtained by the LSFD method satisfy the natural boundary conditions at the free edges without any oscillations.

AB - The Ritz method and some finite element formulations fail to furnish accurate modal stress-resultants for vibrating plates with free edges, even though the natural frequencies and mode shapes are accurately obtained. For example, by using the Ritz method, it was found that the modal twisting moments and shear forces violate the natural boundary conditions and that they contain erroneous "oscillations". This paper presents the least squares finite difference (LSFD) method for solving the freely vibrating plate problem. It will be shown herein that the modal stress-resultants obtained by the LSFD method satisfy the natural boundary conditions at the free edges without any oscillations.

UR - http://www.scopus.com/inward/record.url?scp=33751405071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751405071&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2006.08.055

DO - 10.1016/j.compstruc.2006.08.055

M3 - Article

AN - SCOPUS:33751405071

VL - 84

SP - 2329

EP - 2339

JO - Computers and Structures

JF - Computers and Structures

SN - 0045-7949

IS - 31-32

ER -