Abstract: In this study, the frequencies and mode shapes of thin rectangular plates have been obtained using the Rayleigh Ritz method and characteristic orthogonal polynomials for plates of various boundary conditions. The maximum and minimum frequencies of 23.95 and 9.43 rad/sec were obtained for reinforced concrete plates with all round rigid fixity for aspect ratios of 0.5 and 1.0 respectively. These results clearly demonstrate the crucial role of aspect ratios and boundary restraints. Plates with CCSS and CSCS edge restraints yielded intermediate values of fundamental frequencies with the plate with similar restraints on contiguous sides showing the lesser values. It is noteworthy that plate clamped on opposite side and simply supported on the opposite side gave a maximum frequency almost equal to that for all round clamped plate. Rectangular plates with simply supported edges showed the least values of maximum and minimum of 12.08 and 5.17 rad/sec for aspect ratio of 0.5 and 1.0 respectively. The mode shapes followed a sequence of transverse vibrations along the longitudinal, transverse and diagonal axes of the plates. However, there were variations dependent on aspect ratio and boundary conditions. The output of the proposed model is in close agreement with those of other researchers and standard computer software.
Keywords: The Rayleigh-Ritz, characteristic orthogonal polynomials, reinforced concrete, rectangular plates, vibration, ANSYS.
Title: Dynamic Response of Rectangular Orthotropic Plates Based on Characteristic Orthogonal Polynomials and Rayleigh-Ritz Model
Author: M. E. Ephraim, T. Ode, C. A. Ohia
International Journal of Civil and Structural Engineering Research
ISSN 2348-7607 (Online)
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