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In the recent past, it has been observed that the research in the field of vibration is unceasingly accruing immense importance in the modern science, due to the significant role in every field of applied sciences. As fundamental structural elements, plates of various geometries are widely used in various engineering fields such as, aerospace technology, missile technology, naval ship design and telephone industry etc. Due to the appropriate variation of plate thickness, these plates provide the advantage of reduction in weight and size, and also have significantly greater efficiency for vibrations as compared to the plate of uniform thickness.