Abstract
In the present paper, asymmetric vibration of polar orthotropic annular circular plates of quadratically varying thickness resting on Winkler elastic foundation is studied by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Convergence of the results is tested and comparison is made with results already available in the existing literature. Numerical results for the first ten frequencies for various values of parameters describing width of annular plate, thickness profile, material orthotropy and foundation constant for all three possible combinations of clamped, simply supported and free edge conditions are shown and discussed. It is found that (a) higher elastic property in circumferential direction leads to higher stiffness against lateral vibration; (b) Lateral vibration characteristics ofF-Fplatesis more sensitive towards parametric changes in material orthotropy and foundation stiffness thanC-CandS-Splates; (c) Effect of quadratical thickness variation on fundamental frequency is more significant in cases ofC-CandS-S platesthan that ofF-Fplates. Thickness profile which is convex relative to plate center-line tends to result in higher stiffness of annular plates against lateral vibration than the one which is concave and (d) Fundamental mode of vibration ofC-CandS-Splatesis axisymmetrical while that ofF-Fplatesis asymmetrical.
Highlights
Annular circular plate is the simplest and widely used structural element in various engineering fields
Asymmetric vibration of annular plates of polar orthotropic material having quadratically varying thickness along radial direction and resting on Winkler elastic foundation is analyzed by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method
Rayleigh- Ritz method with orthonormally generated boundary characteristic polynomials has been used to determine natural frequencies and mode shapes of annular circular plates resting on elastic foundation with C-C, S-S and F -F edge conditions
Summary
Annular circular plate is the simplest and widely used structural element in various engineering fields. Gorman [16] employed finite element method to compute natural frequencies of axisymmetric and asymmetric modes of polar orthotropic annular plates of linearly varying thickness, Raju et al [21] used the same technique to analyze axisymmetric vibration of linearly tapered isotropic annular plates. Chen and Ren [27] studied lateral vibration of isotropic and orthotropic thin annular and circular plates of arbitrarily varying thickness along radius using finite element method and obtained natural frequencies and mode shapes of the axisymmetric and asymmetric modes. Asymmetric vibration of annular plates of polar orthotropic material having quadratically varying thickness along radial direction and resting on Winkler elastic foundation is analyzed by using boundary characteristic orthonormal polynomials in Rayleigh-Ritz method. Figures are shown for nodal lines and their corresponding three dimensional mode shapes
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