Fixed-fixed Boundary Conditions Research Articles

Application of nonlinear finite strip technique to concrete deep beams

The salient features of an alternative version of the nonlinear finite strip method for analysing reinforced concrete elements is presented. Unlike the conventional finite strip models which can only handle structures whose geometry does not change in one direction, the newly developed finite strip model can analyse certain structures whose geometry (although still fairly simple) can change along their length such as deep beams with local changes of crosssection along their span(s). Moreover, unlike the conventional finite strip models, the new alternative model has the desirable feature of being able to incorporate any desired boundary conditions and different number of harmonics in various strips with minimal effort. Although the proposed model may, in certain cases, suffer when compared with the conventional alternatives, from the potential drawback of an increased number of strips with associated increases in computer storage, the present model needs many less displacement parameters at each nodal line because of the often substantially shorter lengths of the finite strips (cf. conventional strips) and, hence, needs a much narrower half-bandwidth (HBW) in the stiffness matrix with obvious savings in the subsequent computer running time. Very encouraging correlations have been found between predictions based on the present model and some recently reported test data on deep beams: these include continuous RC deep beams with changes of cross-sections over the supports and also simply supported RC deep beams covering a wide range of design parameters. In addition, the present method has been used to analyse data from a series of tests on RC deep beams with fixed-fixed boundary conditions. The numerical results for deep beams with fixed-fixed boundary conditions based on the present model provide a desirable double check on the validity of a recently reported, largely hand-based, method and should be valuable in identifying the areas in which further work may be required.

Investigation of natural frequencies and mode shapes of buckled beams

The linear modes of vibration of buckled beams are investigated analytically and experimentally. Assuming a static buckled shape corresponding to the nth buckling mode, an exact solution is obtained for the linear modes and associated frequencies of initially buckled beams with fixed-fixed, fixed-hinged, and hinged-hinged boundary conditions. The analytical solution for a first-mode buckled beam is validated experimentally for the fixed-fixed case. The analytically obtained natural frequencies are in excellent agreement with those obtained experimentally. These exact linear modes provide a basis from which to study the nonlinear vibrations of buckled beams.

Vibration And Damping Of A Bonded Tubular Lap Joint

In this paper, a mathematical model to study the transverse vibration and damping of an adhesively bonded tubular lap joint is presented. The governing equations of motion of the system for the case of forced vibration are first derived using the energy method and Hamilton's principle. It is assumed that the energy dissipated by the joint system is contributed by both the shear and bending deformation of the adhesive layer. By using the finite difference method, the numerical solutions of the governing equations for free vibration under fixed-fixed boundary conditions are obtained. The effects of structural parameters and material properties of the adhesive layer on the system modal loss factors and resonance frequencies are also studied.

Vibrothermography: investigation, development and application of a new nondestructive evaluation technique : Henneke, E.G. II; Reifsnider, K.L.; Stinchcomb, W.W. Virginia Polytechnic Institute and State University, Blacksburg (United States), AD-A175-373, 23 pp. (26 Nov. 1986)

Abstract : A summary is presented of the major findings of a program whose objective was to investigate the phenomenon of preferential heat generation around damaged regions in composite materials subjected to mechanical vibrations and to develop an understanding of the mechanisms involved in this process. Vibrothermography is a nondestructive inspection technique based upon the utilization of this phenomenon. It has been found that this technique has considerable potential for inspecting composite materials. A significant amount of knowledge has been gained concerning the nature of the heat generation process and the relation of the frequency dependence of the heat patterns to the mechanical excitations. In particular, we how have convincing evidence that the heat generation around a delamination-type defect occurs preferentially at frequencies corresponding to natural resonance modes of anisotropic plates having the size of the delamination and subjected to fixed-fixed boundary conditions.

Design of a laminated composite with controlled-damage concept

Effects of adhesive strips embedded at the interface in graphite/epoxy laminates on damage tolerance are investigated. Specimens were impact tested under approximately fixed-fixed boundary conditions. Comparisons were made between the specimens with and without the adhesive from X-ray radiographs. Delamination plotted against velocity shows substantially reduced delamination in specimens with adhesive compared with specimens without adhesive. It was observed that below a certain velocity the adhesive acts as a softening strip which confines the delamination to the area of the mesh formed by the adhesive. Three-point-bend tests show that the failure load of plain specimens is higher than for the specimens with adhesive before impact; however, after impact the strength degradation is more severe in the plain specimens. Damage mechanisms of impacted specimens were examined through the use of microphotographs.

Vibrations of slack cables with discrete masses

This paper describes a new method for obtaining the natural frequencies and mode shapes of arbitrarily slack cables which may contain concentrated masses as well as distributed mass and tensile stiffness. The method of imaginary reactions is used to perform the static calculation and Stodola's method is applied to do the dynamics. Integral formulas for the required influence functions appropriate to both fixed-fixed and fixed-forced boundary conditions are included. Solutions to sample problems, obtained with a program implemented on Naval Research Laboratory's Advanced Scientific Computer, are presented. The efficiency of this method is believed to exceed that of available finite element programs when the required number of integration intervals is large: that is, when numerous masses are present and/or high order modes are required.