In-plane free vibration of circular disks using characteristic orthogonal polynomials in Rayleigh-Ritz method

Salem Bashmal, Rama Bhat, Subash Rakheja


The natural frequencies of circular disks subject to various combinations of boundary conditions, with relative ease and acceptable accuracy are studied. Boundary characteristic orthogonal polynomials are used as the admissible functions, which have some advantageous features such as relative ease of generation and integration, diagonal mass matrix and diagonally dominant stiffness matrix. The Rayleigh-Ritz method is employed to solve for the eigenvalues. As an alternative approach, orthogonal polynomials generated for free conditions can be used as trial functions for the clamped case through the use of artificial springs. It is observed that with the increase of the radius ratio, the parameters monotonically increase except for the free-free disks.


Boundary conditions; Eigenvalues and eigenfunctions; Functions; Parameter estimation; Springs (components); Stiffness; Acceptable accuracy; Admissible functions; Artificial springs; Circular disks

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