Abstract
This paper presents a method for the free transverse vibration analysis of thin, elastic, isotropic, uniform and non-uniform circular and annular plates. The circumferential mode numbers (n=0) and (n=1) are dealt with in this paper. The method is a hybrid of plate theory and finite element analysis. The plate is subdivided into one circular and many annular finite elements. Two new finite elements were developed, the first type being a circular plate and the second an annular plate, the displacement functions of the finite element model are the classical solution shape functions of plate theory. Mass and stiffness matrices are determined by precise analytical integration. The free vibrations of uniform circular and annular plates are studied by this method as well as non-uniform plates. The results obtained reveal that the frequencies calculated by this method are in good agreement with those obtained by other authors. This method combines the advantages of the standard finite element analysis and the high-accuracy formulation provided by the use of displacement functions derived from plate theory instead of the usual low-order polynomials. The present method is remarkable for the fact that it enables us to determine with equal precision both low and high natural frequencies.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
