E. Romanelli

Vibrations of rectangular plates elastically restrained against rotation along all edges and subjected to a bi-axial state of stress

Simple polynomial approximations and Galerkins method are used to determine the fundamental frequency of vibration of thin, elastic plates with symmetric slope restraints and subjected to a bi-axial state of tensile stresses, Nx, and Ny. Two other frequencies of higher order are determined by following the same approach. It is hoped that mechanical engineers will find useful the frequency expressions obtained in the present study in view of their simplicity and high accuracy.

On the analysis of waveguides of doubly-connected cross-section by the method of conformal mapping

Abstract This paper deals with the determination of cutoff frequencies in waveguides of arbitrary, doubly-connected cross-section. The given domain is transformed into an annular region and the transformed partial differential equation is solved by means of a variational technique. Calculations are presented for acoustically soft waveguides of regular polygonal shape with circular inner boundaries. The problem is mathematically equivalent to the determination of TM modes in electromagnetic waveguides.

Fundamental frequencies of non-circular, elastic, hinged arcs

Abstract Lowest natural frequencies of elastic hinged arcs are calculated by using Rayleighs principle. The effect of variable curvature is taken into account and the results are compared with values available in the open literature.

A note on the fundamental frequency of circular membranes with a class of boundary disturbances

The present note deals with the calculation of natural frequencies of vibrating circular membranes with periodic disturbances in the boundary. The given shape is mapped onto a unit circle in the -plane by a two-term polynomial. Galerkins method is used to solve the transformed differential system.