Some studies on the response of a tapered beam
TL;DR: In this article, a detailed study on the effect of different types of thickness profiles on the response of a beam was conducted and the results obtained for different thickness profiles are compared with those obtained for parallel beam.
About: This article is published in Computers & Structures.The article was published on 1992-09-17. It has received 7 citations till now. The article focuses on the topics: Beam (structure).
Citations
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TL;DR: In this paper, the debonding strength of axially loaded double shear lap specimens between steel plates and carbon fibre reinforced plastic plates is investigated from the analytical, numerical and experimental point of view.
87 citations
TL;DR: In this article, the effect of taper and tip thickness on the maximum resonant stress of a tapered beam subjected to externally applied harmonic pressure distributions and to investigate its possible implications to blade vibration was determined.
Abstract: The objective of the work reported here is to determine the effect of taper and tip thickness on the maximum resonant stress of a tapered beam subjected to externally applied harmonic pressure distributions and to investigate its possible implications to blade vibration. Tapered beams are of interest since their geometry is similar to that of the leading or trailing edge of an airfoil. As a result, airfoil chordwise bending modes should exhibit similar sensitivity to changes in chordwise taper and leading or tailing edge thickness. As a result, the tapered beam provides a simplified, first-order model of an airfoil`s behavior that should provide insight into the sensitivity of the airfoil`s response to geometric perturbations. The sensitivity of the response to geometric changes also depends on the type of excitation that is applied. The spatial distributions of the excitation pressures used in this study are: a constant pressure to serve as a baseline, a leading edge type pressure distribution, and a trailing edge type pressure distribution. Consequently, the relative importance of each type of excitation in terms of how it affects tip mode response will be assessed.
7 citations
TL;DR: In this article, a beam element with 2 DOF (degrees of freedom) per node is used for the analysis of three beam models with discontinuity in the thickness and subjected to harmonic point load.
5 citations
TL;DR: Forced axisymmetric response of a circular plate of linearly varying thickness, based on the classical theory, is analyzed by the eigen-function method as mentioned in this paper, and exact solution for the free vibration mode shapes is obtained by the Frobenius method.
3 citations
TL;DR: In this paper, three beam models are analyzed for possible reduction of maximum displacement and maximum stress by choosing the discontinuity at different locations, and numerical results are presented for various step-ratios in the thickness.
3 citations
References
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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