International Journal of Civil and Structural Engineering Research ISSN 2348-7607 (Online) Vol. 7, Issue 1, pp: (16-22), Month: April 2019 - September 2019, Available at: www.researchpublish.com
Determination of Resonating Frequency of Thin Rectangular Flat Plates Edward I. Adah1, Owus. M. Ibearugbulem2, David. O. Onwuka3, Solomon U. Okoroafor4 1
Department of Civil and Environmental Engineering, University of Calabar, Nigeria
2, 3, 4
Department of Civil Engineering, Federal University of Technology, Owerri, Nigeria
Abstract: The development of a general computer program for analysis of free vibration of rectangular thin plates using polynomial functions is the focus of this study. A general polynomial shape function was first derived and then Ritz energy equation used to obtain an equation in terms of a non-dimensional parameter 'k', for the resonating frequency of a vibrating plate. Thereafter, Matlab programming language was used to develop an interactive computer program which requires the user to input the shape function and dimensions of each plate under consideration in order to obtain the resonating frequency. The validity of the program was demonstrated by comparing the predicted resonating frequencies with those obtained by other relevant researchers. The percentage differences were minimal and insignificant. Thus, the developed program can be used for easy and quick free vibration analysis of rectangular plates. Keywords: Determination, Matlab Programming, Polynomial Shape Function, Resonating Frequency, Rectangular Plate, Ritz Energy Equation, Free Vibration. Symbols w = Deflection; wmax = Maximum Deflection; U, V= Deflection parts in X- & Y- Directions for Non-dimensional Parameters R or r = Non dimensional Parameter in X- direction and is equal X/a Q or q = Non dimensional Parameter in Y- direction and is equal Y/b a = dimension along X -direction; b = dimension along Y- direction w''R =
;
w''Q =
; w''RQ =
; k''R =
;
k''Q =
; k''RQ =
ρ = Specific Gravity of plate material, h = plate thickness; D = flexural rigidity.
1. INTRODUCTION Free vibration of rectangular plate can be studied by specifying the boundary conditions of a plate. Often times, undesirable excitations both internal and external, have been experienced by structural elements such as plates. The most important thing in the analysis of free vibration, is the resonating frequency, which is the value of externally induced vibrating frequency on the plate that causes it to resonate. [1], [2], [3], [4], [5], [6] and many other scholars have carried out studies on free vibration of plates using classical and approximate methods based on trigonometric shape function. And of most recent scholars like [7], [8], [9], [10], [11], did such analysis in a different way using polynomial shape functions. [12], [13] tried applying the used of programing method in CCCC plate analysis. But, there is dearth of literature on the development of computer programs based on polynomial functions to ease the difficulties of the former approaches. Therefore, the purpose of the present study is to design a computer program for easy, quick and inexpensive free vibration analysis of rectangular plates.
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