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

doi:10.1016/j.compstruc.2006.08.055

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 journal › Article › peer-review

7 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 language	English
Pages (from-to)	2329-2339
Number of pages	11
Journal	Computers and Structures
Volume	84
Issue number	31-32
DOIs	https://doi.org/10.1016/j.compstruc.2006.08.055
Publication status	Published - Dec 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

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10.1016/j.compstruc.2006.08.055

Cite this

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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",

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language = "English",

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AU - Wang, C. M.

AU - Wu, W. X.

AU - Shu, C.

AU - Utsunomiya, T.

PY - 2006/12

Y1 - 2006/12

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.

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SN - 0045-7949

VL - 84

SP - 2329

EP - 2339

JO - Computers and Structures

JF - Computers and Structures

IS - 31-32

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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