Free vibration analysis of circular plates using generalized differential quadrature rule.

*(English)*Zbl 1083.74549Summary: The free vibration of solid circular plates has been studied using the generalized differential quadrature rule (GDQR). The effects such as stepped thickness, intermediate concentric ring supports, and elastic restraints have been considered. Discrete system equations for natural frequency analysis were derived based on the GDQR. Issues related to the implementation of the boundary and compatibility conditions were addressed. Two regularity conditions at the solid circular plate center were formularized, since they were not quite clear in the present literature. Some wrong applications in the implementation of both differential quadrature methods and regularity conditions at the solid circular plate center have been pointed out. Excellent results have been obtained with the presented examples.

##### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74K20 | Plates |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |

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\textit{T. Y. Wu} et al., Comput. Methods Appl. Mech. Eng. 191, No. 46, 5365--5380 (2002; Zbl 1083.74549)

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##### References:

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