DYNAMICS OF RECTANGULAR ORTHOTROPIC PLATES USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL – GALERKIN’S METHODS

Authors

  • NN Osadebe DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA. ENUGU STATE, NIGERIA
  • CM Attama DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA. ENUGU STATE, NIGERIA
  • OA Oguaghamba DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA. ENUGU STATE, NIGERIA

DOI:

https://doi.org/10.4314/njt.361.1213

Keywords:

Fundamental natural frequency, Free Vibration, Reinforced Concrete Slab, Characteristic Orthogonal Polynomial

Abstract

The assumed deflection shapes used in the approximate methods such as in the Galerkin’s method were normally formulated by inspection and sometimes by trial and error, until recently, when a systematic method of constructing such a function in the form of Characteristic Orthogonal Polynomial (COPs) was developed by Bhat in 1985. In the vibrational analyses of orthotropic rectangular plates with different boundary conditions, the study used the characteristic orthogonal polynomial theory to obtain satisfactory approximate shape functions for these plates. These functions were applied to Galerkin indirect varational method to obtain new set of fundamental natural frequencies for these plates. The results were reasonable when compared with those in the previous work. All round simply supported thin rectangular plate (SSSS), rectangular clamped plated (CCCC) and rectangular plate with one edge clamped and all others edges simply supported (CSSS) gave 5.172, 9.429 and 6.202 natural frequencies in rad /sec respectively at 0.05%, 0.0% and 22.93% difference with the previous[3] results5.170rad/sec, 9.429rad/sec and 8.048rad/sec  for SSSS, CCCC and CSSS. For others like: rectangular plate with one edge simply supported and all other edges clamped (CCSC), rectangular plate simply supported at two opposite sides and clamped at the others (CSCS) and rectangular plate clamped at two adjacent sides and simply supported at the others (CCSS) with no available results, their natural frequencies obtained are 8.041rad/sec, 6.272rad/sec and 7.106rad/sec respectively.

 

http://dx.doi.org/10.4314/njt.v36i1.8

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Section

Building, Civil & Geotechnical Engineering

How to Cite

DYNAMICS OF RECTANGULAR ORTHOTROPIC PLATES USING CHARACTERISTIC ORTHOGONAL POLYNOMIAL – GALERKIN’S METHODS. (2016). Nigerian Journal of Technology, 36(1), 50-56. https://doi.org/10.4314/njt.361.1213

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