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1 Journal of Applied Analysis

1 2022

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Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness

Singh Robin, Dhiman Neeraj, Tamsir Mohammad

Journal of Applied Analysis

2022

Vol. 28, nr 2

263--273

Mathematical model to account for non-homogeneity of plate material is designed, keeping in mind all the physical aspects, and analyzed by applying quintic spline technique for the first time. This method has been applied earlier for other geometry of plates which shows its utility. Accuracy and versatility of the technique are established by comparing with the well-known existing results. Effect of quadratic thickness variation, an exponential variation of non-homogeneity in the radial direction, and variation in density; for the three different outer edge conditions namely clamped, simply supported and free have been computed using MATLAB for the first three modes of vibration. For all the three edge conditions, normalized transverse displacements for a specific plate have been presentedwhich shows the shiftness of nodal radii with the effect of taperness.