Transverse vibrations and elastic stability of circular plates of variable thickness and with non-uniform boundary conditions

✍ Scribed by P.A.A. Laura; G.M. Ficcadenti

• Publisher: Elsevier Science
• Year: 1981
• Tongue: English
• Weight: 338 KB
• Volume: 77
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(81)80167-8

✦ Synopsis

An approximate method is presented for dealing with transverse vibrations of cirRular plates of variable thickness in the case of supports having rotational flexibility which varies in an arbitrary manner around the boundary. It is also assumed that the plate is subjected to a hydrostatic state of in-plane stress; accordingly the buckling coefficient is obtained by setting the frequency coefficient equal to zero in the frequency determinant.

A unified yet simple and straightforward approach has been developed in order to solve this rather difficult elastomechanics problem. The method consists in representing the varying stiffness in terms of a Fourier expansion in the polar angle and expressing approximately the displacement function by using a summation of polynomial co-ordinate functions which satisfy exactly only the eisential boundary condition. The Ritz method is then applied in order to obtain the frequency determinant. The method can be easily extended to the forced vibrations case.