Dynamic Response of Thick Rectangular Orthotropic Plates Based on Characteristics Orthogonal Polynomial and Rayleigh-Ritz Model
Abstract
This study investigates the dynamic behavior of thick rectangular orthotropic plates subjected to free undamped vibration. An analytical derivation of natural frequency was carried out based on characteristics orthogonal polynomial and Rayleigh-Ritz method. To investigate the effect of plate boundary conditions on the natural frequency. Two boundary conditions namely: plate clamped around the four edges , and plate simply supported around the four edges where investigated. To establish a comparative study, finite element simulation (Eigen value modal analysis) was carried out using ANSYS software. The two boundary conditions were modeled and compared to the analytical results. The effect of aspect ratios on the natural frequencies were investigated. Plate clamped around the four edges showed the maximum and minimum frequency of 130.097 and 96.937 rad/sec with aspect ratio of 0.5 and 1.0 respectively. Plate simply supported around the edges showed the least value of maximum and minimum frequency of 94.405 and 65.844 rad/sec with aspect ratio of 0.5 and 1.0 respectively. The results showed that natural frequency decreases as the aspect ratio increases. This implies that the bending stiffness of the plate decreases as the aspect ratio increases. The modal output showed the same characteristics with the results obtained from the previous research. The difference between the proposed model ANSYS and the analytical calculation is less than 10%
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