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Adah, E. I.
Department of Civil and Environmental Engineering, University of Calabar, Nigeria.
Okere, C. E.
Department of Civil Engineering, Federal University of Technology Owerri, Nigeria.
Ibearugbulem, O. M.
Department of Civil Engineering, Federal University of Technology Owerri, Nigeria.
Ezeanyagu, C. F.
Department of Civil and Environmental Engineering, University of Calabar, Nigeria.
Umunnah, R. A.
Department of Mechanical Engineering, University of Calabar, Nigeria.
ABSTRACT
The
purpose of this work is to formulate specific mathematical models for the
analysis of thin rectangular plates with one free edge and to check the
suitability of the new general formulated mathematical model for free vibration
analysis of plates under large displacement for these plate types. The shape
profiles of the six plates under consideration were used to evaluate the
individual plate types' stiffness due to bending and membrane actions. For each
plate type the individual stiffness was substituted into the general
mathematical model and simplified to obtain the specific nonlinear frequency
models for each plate type. Based on the new specific models, the linear and nonlinear
frequencies of these plates under consideration were predicted. To validate
these new equations, numerical analysis was carried out, and the predicted numerical results
for the fundamental frequencies obtained for these plate types were compared with
those in the literature
which were in total agreement with the ones compared with. The maximum
percentage difference of 10.8286% was obtained for a plate Simply supported at
the first and fourth edge, clamped at second edge and free at the third edge (SCFS) and
8.7% obtained for a plate clamped
at first edge, simply supported at
second and fourth edges and free at third edge (CSFS). Theses percentages are
considered adequate statically. Hence, the conclusion that the formulated
general free vibration equation for the analysis of rectangular plate is adequate and that the specific models are satisfactory too, and that the new method is an easy method and saves time.
Keywords: Dynamic Excitation, Membrane strain, mathematical models, nonlinear frequency, rectangular plates.
https://doi.org/10.33922/j.ujet_v9i2_5
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Published
Monday, November 06, 2023
Issue
Vol.9 No.2, December 2023
Article Section
GENERAL
The contents of the articles are the sole opinion of the author(s) and not of UJET.
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