P.A.A. Laura

In-plane vibrations of non-circular arcs of non-uniform cross-section

Abstract The title problem is solved by using polynomial co-ordinate functions and the Ritz method to generate the frequency equation. Symmetric and unsymmetric structural systems are considered. The agreement with results available in the literature or with eigenvalues determined by means of a finite element code is good from an engineering viewpoint.

A review of the acoustic-emission monitoring of wire rope

This review of existing technology on the acoustic-emission inspection of wire rope has confirmed that the most realistic application of the method is in the detection and location of wire breaks. However, the successful detection and location of wire breaks is dependent upon such factors as rope construction, diameter, length and number of wire breaks. The occurrence of large numbers of wire breaks work against the technique; although such large numbers of wire breaks are only likely to be generated in the laboratory during the fatigue testing of rope specimens. This review has shown that acoustic emission can be a useful laboratory tool, but application of the technique to ropes in service will probably be limited and specific to certain applications. In order to develop the technique for practical applications, future work needs to concentrate on the rope constructions that are most commonly used in industry, also those which are best suited to the technique, and developing wire-break signatures that could be designed into future equipment. This can be achieved through narrow-band filters, matching the resonant frequency of the transducers to the main frequency components of a wire break and pattern recognition software.

Calculations of Eigenvalues for Uniform Fluid Waveguides with Complicated Cross Sections

This paper deals with the calculation of eigenvalues of acoustical waveguides with arbitrary cross section. The method presented herein makes use of conformal mapping techniques and Galerkins method to solve the transformed wave equation. Numerical calculations are presented for two types of boundary conditions: (a) zero velocity, and (b) zero pressure at the walls.

Free vibration of rectangular plates with circular openings

The optimized Rayleigh-Ritz method is applied to generate values of the fundamental frequency coefficient and the one corresponding to the first fully antisymmetric mode for rectangular plates elastically restrained against rotation and with located circular holes. The results of this study are compared with existing data and the agreement is quite good.

Vibrations of rectangular plates of bilinearly varying thickness and with general boundary conditions

Abstract Results are presented for the fundamental frequency of a rectangular plate having a thickness which varies in a bilinear fashion in the x -direction. Translational and rotational flexibilities are taken into account at all edges. A simple algorithm, which allows one to evaluate the fundamental frequency of vibration, is derived by making use of the Ritz method and expressing the fundamental displacement function in terms of a polynomial co-ordinate function which satisfies approximately the natural boundary conditions.

Transverse vibrations of plates with stepped thickness over a concentric circular region

Abstract This paper deals with the determination of the fundamental frequency of vibration of: (a) rectangular, (b) regular polygonal and (c) circular plates with stepped thickness over a concentric, circular subdomain of the plates. The problems are solved in a unified fashion by adopting simple polynomial co-ordinate functions and making use of the Ritz method to generate the frequency determinant.

Vibrations of rings of variable cross section

Abstract The present paper deals with the determination of the lower natural frequencies of vibration of rings of variable cross-sectional area using three approximate schemes: • —using polynomial coordinate functions in the angular coordinate in order to approximate the fundamental mode shape • —expanding the ring response in terms of a sinusoidal truncated series • —by means of a finite element algorithm. When using the first two procedures the Ritz method is applied in order to obtain the frequency equation. In general very good agreement is obtained between the eigenvalues predicted by the three approaches.

Numerical experiments on vibrating rectangular plates with discontinuously varying cross sections

Utilisation des methodes de Rayleigh-Ritz et des elements finis. Etude de la plaque encastree et simplement supportee

Free vibrations of rectangular plates elastically restrained against rotation with circular or square free openings

Abstract The fundamental frequency of vibration of plates elastically restrained against rotation along the edges and with centrally located circular or square holes is determined by means of the optimized Rayleighs method. Independent solutions are also obtained using the finite element method. A comparison with experimental values is also presented in the case where the plate is rigidly clamped along the four edges.

A note on free flexural vibrations of a non-uniform elliptical ring in its plane

Abstract An approximate solution for the title problem is obtained by using the Rayleigh-Ritz method. Two different types of co-ordinate functions are used: sinusoids, and polynomial expressions which contain an undetermined exponential parameter which allows for minimization of the natural frequency coefficients. Continuous and discontinuous variation of the ring thickness are considered. The analytical predictions are compared with values obtained by means of the finite element method, and good engineering agreement is shown to exist. No claim of originality is made, but it is hoped that present results will be of interest to designers.