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Free vibration of rectangular plates with a small initial curvatureThe method of matched asymptotic expansions is used to solve the transverse free vibration of a slightly curved, thin rectangular plate. Analytical results for natural frequencies and mode shapes are presented in the limit when the dimensionless bending rigidity, epsilon, is small compared with in-plane forces. Results for different boundary conditions are obtained when the initial deflection is: (1) a polynomial in both directions, and (2) the product of a polynomial and a trigonometric function, and arbitrary. For the arbitrary initial deflection case, the Fourier series technique is used to define the initial deflection. The results obtained show that the natural frequencies of vibration of slightly curved plates are coincident with those of perfectly flat, prestressed rectangular plates. However, the eigenmodes are very different from those of initially flat prestressed rectangular plates. The total deflection is found to be the sum of the initial deflection, the deflection resulting from the solution of the flat plate problem, and the deflection resulting from the static problem.
Document ID
19880020764
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Adeniji-Fashola, A. A. (National Academy of Sciences - National Research Council Washington, DC., United States)
Oyediran, A. A. (Lagos State Univ. Ojo, Nigeria)
Date Acquired
September 5, 2013
Publication Date
August 1, 1988
Subject Category
Structural Mechanics
Report/Patent Number
NAS 1.26:179370
NASA-CR-179370
Accession Number
88N30148
Funding Number(s)
CONTRACT_GRANT: NASW-3458
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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