Free vibration analysis of rectangular plate by Split-Deflection method

This paper presents free vibration analysis of rectangular plate by split-deflection method. In this method, the deflection was split into x and y components of deflection. That is the deflection of the rectangular plate was taken as the product of these two components. Having made this assumption, the study went ahead to formulate total potential energy functional from principles of theory of elasticity based on work-error approach. This energy functional was minimized by direct variation and equation for resonating frequency was obtained. Two illustrative examples were used to test this method. They are plates with all edges simply supported and all edges clamped. The first case used polynomial function for x component of deflection and trigonometric function for y component of. However, the second example used polynomial function for both x and y components of deflection. Fundamental resonating frequencies (in non dimensional forms) of the two plates for aspect ratios ranging from 1.0 to 2.0 (at increment of 0.1) were determined and compared with the values from previous study. From the comparison, it was observed that the maximum percentage difference of 0.06 was recorded for the first example at aspect ratios of 1.1 and 1.3 with non dimensional resonating frequencies of 18.03 and 15.71 respectively. For the second example, the maximum percentage difference of 0.09 was recorded at aspect ratio of 1.1 with non dimensional resonating frequencies of 32.96. This small value of percentage differences show that this present method is adequate and reliable for classical plate theory (CPT) free vibration analysis of rectangular plates.