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Non‐linear random response of laminated composite shallow shells using finite element modal method
Author(s) -
Guo Xinyun,
Lee YiuYin,
Mei Chuh
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1672
Subject(s) - finite element method , equations of motion , modal , vibration , modal testing , stiffness , structural engineering , random vibration , normal mode , shell (structure) , modal analysis , modal analysis using fem , mathematical analysis , mathematics , buckling , physics , materials science , classical mechanics , engineering , acoustics , composite material
This paper investigates the large‐amplitude multi‐mode random response of thin shallow shells with rectangular planform at elevated temperatures using a finite element non‐linear modal formulation. A thin laminated composite shallow shell element and the system equations of motion are developed. The system equations in structural node degrees‐of‐freedom (DOF) are transformed into modal co‐ordinates, and the non‐linear stiffness matrices are transformed into non‐linear modal stiffness matrices. The number of modal equations is much smaller than the number of equations in structural node DOF. A numerical integration is employed to determine the random response. Thermal buckling deflections are obtained to explain the intermittent snap‐through phenomenon. The natural frequencies of the infinitesimal vibration about the thermally buckled equilibrium positions (BEPs) are studied, and it is found that there is great difference between the frequencies about the primary (positive) and the secondary (negative) BEPs. All three types of motion: (i) linear random vibration about the primary BEP, (ii) intermittent snap‐through between the two BEPs, and (iii) non‐linear large‐amplitude random vibration over the two BEPs, can be predicted. Copyright © 2006 John Wiley & Sons, Ltd.