Studies on dynamic behaviour of a beam with symmetrically varying thickness
TL;DR: In this article, a detailed study has been conducted on the effect of different types of variation in profile and thickness on the amplitude and the dynamic bending stress of a beam under a point harmonic load.
About: This article is published in Computers & Structures.The article was published on 1993-04-17. It has received 1 citations till now. The article focuses on the topics: Beam (structure).
Citations
More filters
TL;DR: In this paper, the authors analyzed lateral-torsional dynamic instability of elastic beams with rectangular cross section having constant thickness, with the depth symmetric with respect to the midpoint and either uniform or tapered linearly in each half Free vibrations are also investigated.
1 citations
References
More filters
TL;DR: In this article, the Bernoulli-Euler equation for the free vibrations of a double-tapered cantilever beam is developed from a computer solution of this equation, and a table has been developed from which the fundamental frequency, second, third, fourth, and fifth harmonic can easily be obtained for various taper ratios.
Abstract: The differential equation is developed from the Bernoulli‐Euler equation for the free vibrations of a double‐tapered cantilever beam. The beam tapers linearly in the horizontal and in the vertical planes simultaneously. From a computer solution of this equation, a table has been developed from which the fundamental frequency, second, third, fourth, and fifth harmonic can easily be obtained for various taper ratios. Charts are plotted for selected taper ratios in the vertical plane to show the effect of taper ratios on frequency.
88 citations
TL;DR: Explicit expressions for the element mass and stiffness matrices of a linearly tapered beam finite element including shear deformation and rotary inertia are given in this article, where the element cross section rotation is assumed to be a sum of the slope of the transverse displacement and the shear.
55 citations
TL;DR: In this article, free vibrations of nonuniform cantilever beams with an end support have been investigated, using the equations of Bernoulli-Euler, and two configurations of interest are treated: (a) constant width and linearly variable thickness, and (b) constant thickness and linear variable width.
Abstract: Free vibrations of nonuniform cantilever beams with an end support have been investigated, using the equations of Bernoulli‐Euler. Two configurations of interest are treated: (a) constant width and linearly variable thickness, and (b) constant thickness and linearly variable width. Charts have been plotted for each case from which the fundamental frequency, the second harmonic, and the third harmonic can be easily determined for various taper ratios. The Tables from which these charts were plotted are also included.
53 citations
TL;DR: In this paper, the effect of shear deformation upon the natural frequencies of a beam with classical boundary conditions can be estimated within the limits of practical accuracy by using a simple formula similar to the one used for simply supported beams.
36 citations
TL;DR: In this paper, a procedure based on the Galerkin method is employed to estimate the first few natural frequencies of a beam with varying sectional properties and including the effects due to rotary inertia.
28 citations