Optimization of Plate Vibration Based on Innovative Elliptical Thickness Variation - Neeraj Lather; Naveen Mani; Rahul Shukla; Amit Sharma (AppliedMath, 2025)
This study innovatively explores vibrational control with reference to elliptical thickness variation. Traditionally, plate vibrations have been analysed by incorporating circular, linear, parabolic, and exponential thickness variations. However, these variations often fall short in optimizing vibrational characteristics. So, we develop a new formula specifically for orthotropic as well as isotropic plates with elliptical thickness profiles and employ the Rayleigh–Ritz method to calculate the vibrational frequencies of the plate. This research demonstrates that elliptical variation significantly reduces vibrational frequencies compared to conventional thickness profiles. The findings indicate that this unique configuration enhances vibrational control, offering potential applications in engineering fields where vibration reduction is essential. The results provide a foundation for further exploration of non-standard thickness variations in the design of advanced structural components. The study reveals that the elliptical variation in tapering parameter is a much better choice than other variation parameters studied in the literature for the purpose of optimizing the vibrational frequency of plates.