Daniel R. Avalos

Analytical and experimental investigation on vibrating circular plates with stepped thickness over a concentric circular region

Transverse vibrations of the structural elements described in the title are studied for the case where the edges are elastically restrained against translation and rotation. Since finding an exact solution is a difficult task, it was considered convenient to approximate the response of the plate in the case of free, axisymmetric vibrations by means of a summation of simple polynomial coordinate functions that satisfy the governing boundary conditions. The Ritz method is used in order to generate the frequency equation. The natural frequency coefficients are optimized by minimizing each eigenvalue with respect to an undetermined exponential parameter included in each coordinate function.

Vibrations of a simply supported plate carrying an elastically mounted concentrated mass

Abstract A large number of papers and technical reports are available on the technically important problem of structural elements executing transverse vibrations and carrying concentrated masses. In general it is assumed that the attachment is perfectly rigid. On the other hand, a rather limited amount of published work is available when the mass is elastically connected to the structure. The system then exhibits a more complex behavior than in the case of rigid attachment. The present study deals with the solution of the title problem using the well-known normal mode, sinusoidal eigenfunction expansions.

Vibrating circular plates with stepped thickness over a concentric circular region: a general, approximate solution

Natural frequencies corresponding to axi‐ and antisymmetric modes of vibration of the structural elements described in the title are studied using the optimized Rayleigh–Ritz approach. It is assumed that the plates are elastically restrained against translation and rotation. The plate amplitude is approximated in terms of polynomial coordinate functions that satisfy the boundary conditions, each one containing an undetermined exponential parameter that allows for the minimization of the eigenvalues under investigation.

Natural frequencies of a Bernoulli beam carrying an elastically mounted concentrated mass

Abstract Civil, naval and ocean engineers are frequently confronted with the problem of mounting dynamic, operational units on structural elements. The designer must be able to determine natural frequencies of the coupled system: structure-motor or engine and its elastic mounting. Frequency coefficients are obtained in the present study for three combinations of boundary conditions: simply supported; simply supported and clamped at both ends.

Transverse vibrations and buckling of circular plates of discontinuously varying thickness subject to an in-plane state of hydrostatic stress

Natural frequencies and buckling loads of circular plates with stepped thickness over a concentric circular region are determined using the optimized Rayleigh-Ritz method. The solution is obtained for the case of edges elastically restrained against rotation and translation.

A low-cost fiber-optic system for monitoring the state of structural health of a mechanical cable

Abstract Methods for evaluating the structural health of mechanical cables and detecting their imminent failure could prevent the loss of valuable equipment and, more importantly, the possible loss of human life. The non-destructive test methods available are: thorough visual examination and measurement of the external diameter; X-rays; (induced) wave propagation; acoustic emission; magnetostrictive sensors; infrared detection. A new method which employs a commercial optical fiber for detecting the breakage of individual wires in a rope is proposed in the present paper.

Dynamic stiffening of circular plates and determination of their buckling, in-plane pressure

Abstract This paper presents some numerical experiments performed on transverse vibrations and the elastic stability of homogeneous, isotropic, clamped circular plates of discontinuously varying thickness. The purpose of the study is threefold: (1) to determine dynamic stiffening situations; (2) to experiment on the effect of optimization with respect to an exponential parameter (non-integer version of the Rayleigh-Ritz method or the ‘optimized Rayleigh-Ritz method’) as opposed to the classical version of the energy method; and (3) to ascertain the relative accuracy of the optimized Rayleigh-Ritz method by comparing eigenvalues determined using this technique and those calculated using a very efficient standard finite element code.

Free and forced vibrations of a simply supported rectangular plate partially embedded in an elastic foundation

Abstract The present note deals with an approximate solution of the title problem in the case where a portion of the plate is subject to a p o cos ωt-type excitation. The lower natural frequency coefficients and dimensionless values of displacements and stress resultants are determined for several combinations of the mechanical parameters coming into play.

Fundamental frequency of rectangular membranes with a boundary perturbation

Abstract An approximate solution to the title problem is presented. The results, obtained by the Galerk in method and using polynomial approximations, are compared with values obtained by means of a finite element algorithm.

Variational analysis of a model for a piezoelectric polymer flexural plate hydrophone

An approximate solution for the mathematical model of the piezoelectric polymer flexural plate hydrophone is presented. The case where sheets of polymer are attached to air‐backed rectangular flexural plates is treated. This study constitutes an extension of Ricketts’ recent treatment in the sense that (a) dynamic effects are now taken into account and (b) simply supported, clamped, or elastically restrained edges are now considered.