Exact closed form solution for the analysis of the transverse vibration modes of a Timoshenko beam with multiple concentrated masses

Torabi, Keivan; Jazi, Adel Jafarzadeh; Zafari, Ehsan

doi:10.1016/j.amc.2014.04.019

Cited by 19 publications

(16 citation statements)

References 16 publications

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“…(21) into (13) together with the boundary conditions (17) will define the resonances frequencies of the linear modes Φ i (x), which will correspond to the zeros of the corresponding determinant. A similar solution for an unbuckled simple clamped-clamped beam with an attached point-like masses was obtained for the Timoshenko beam in [24].…”

Section: Linear Vibration Modes Of the Absorbersupporting

confidence: 57%

Bistable nonlinear damper based on a buckled beam configuration

Iurasov

Mattei

2019

Nonlinear Dyn

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This article addresses a particular realization of a compact bistable nonlinear absorber based on the concept of Nonlinear Energy Sink. The article presents both a detailed description of the absorber mechanics and an illustration of the targeted energy transfer between the absorber and a linear system. The experimental results are accompanied with the numerical simulations. Beside practical improvements linked to the features of absorber design, the obtained results stay in line with those found for simpler realizations of a bistable Nonlinear Energy Sinks.

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Section: Linear Vibration Modes Of the Absorbersupporting

confidence: 57%

Bistable nonlinear damper based on a buckled beam configuration

Iurasov

Mattei

2019

Nonlinear Dyn

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“…The difference between theoretical results and experiment is about 5%, 11%, 17% for CF and 9%, 15%, 14% for CC in the first, second and third modes, respectively. This difference may be due to the effect of the accelerometer sensor attached on the specimens, which acts as a concentrated mass (1 g) [37]. Since the location of the sensor, as a concentrated mass, is the same in all specimens (at the point of a quarter of the length), the value of frequency reduction in the intact and delaminated beams are equal and has no influence on measured frequency reduction in delaminated specimen rather than intact one.…”

Section: Effect Of Lengthwise Location and Small Size Of Delaminationmentioning

confidence: 99%

Experimental and theoretical investigation on transverse vibration of delaminated cross-ply composite beams

Torabi

Samadi

Heidari-Rarani

2016

International Journal of Mechanical Sciences

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“…After the foregoing manipulations, the whirling motion of a rotating three‐dimensional (3D) shaft mounted by any number of rigid disks is similar to the transverse vibration of a stationary two‐dimensional (2D) beam carrying any number of concentrated elements. Finally, the methods presented by the researchers 29‐34 for the free vibration analyses of a stationary 2D beam carrying various concentrated elements can be used to determine the forward and backward whirling speeds and the associated whirling mode shapes of a loaded rotating 3D shaft. In addition to comparing with the existing literature, all results obtained from the presented method are also compared with those obtained from the FEM 35 and good agreements are achieved.…”

Section: Introductionmentioning

confidence: 99%

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

Hsu

2020

Engineering Reports

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In theory, the whirling motion of a shaft-disk system is three-dimensional (3D), however, if the transverse displacement in the vertical principal xy-plane and that in the horizontal principal xz-plane for the cross-section of the shaft located at the axial coordinate x are represented by a complex number, then the mass moment of inertia for unit shaft length (at x) and that for each rigid disk i can be combined with their associated gyroscopic moments (GMs) to form the frequency-dependent equivalent mass moments of inertia, respectively, in the equations of motion for the rotating Timoshenko shaft carrying arbitrary rigid disks. It is found that the above-mentioned equations for the rotating 3D shaft-disk system take the same forms as the corresponding ones for the associated stationary two-dimensional (2D) Timoshenko beam carrying the same number of disks, so that the approaches for the free vibration analyses of the stationary 2D beam-disk system can be used to solve the title problem for obtaining the whirling speeds and mode shapes of a rotating 3D shaft-disk system. Since the order of the eigenproblem equation derived from the presented approach is much smaller than that derived from the conventional finite element method (FEM), the computer time consumed by the former is much less than that by the latter. In addition, the solutions obtained from the presented approach are exact and may be the benchmark for evaluating the accuracy of solutions of the other approximate methods. Numerical examples reveal that the presented approach is available for the uniform or nonuniform shaft-disk system, and the obtained results are very close to those obtained from existing literature or the FEM. The formulation of this article is available for a shaft-disk system with various boundary conditions (BCs), to save space, only the cases with pinned-pinned BCs are illustrated. K E Y W O R D S Timoshenko shaft, gyroscopic moment, equivalent mass moment of inertia, whirling speeds and mode shapes This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Exact closed form solution for the analysis of the transverse vibration modes of a Timoshenko beam with multiple concentrated masses

Cited by 19 publications

References 16 publications

Bistable nonlinear damper based on a buckled beam configuration

Bistable nonlinear damper based on a buckled beam configuration

Experimental and theoretical investigation on transverse vibration of delaminated cross-ply composite beams

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

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