In-plane free vibration of circular disks using characteristic orthogonal polynomials in Rayleigh-Ritz method
Keywords:Boundary conditions, Eigenvalues and eigenfunctions, Functions, Parameter estimation, Springs (components), Stiffness, Acceptable accuracy, Admissible functions, Artificial springs, Circular disks
AbstractThe 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.
How to Cite
Copyright on articles is held by the author(s). The corresponding author has the right to grant on behalf of all authors and does grant on behalf of all authors, a worldwide exclusive licence (or non-exclusive license for government employees) to the Publishers and its licensees in perpetuity, in all forms, formats and media (whether known now or created in the future)
i) to publish, reproduce, distribute, display and store the Contribution;
ii) to translate the Contribution into other languages, create adaptations, reprints, include within collections and create summaries, extracts and/or, abstracts of the Contribution;
iii) to exploit all subsidiary rights in the Contribution,
iv) to provide the inclusion of electronic links from the Contribution to third party material where-ever it may be located;
v) to licence any third party to do any or all of the above.