The influence of axial load on eigen-frequencies of a vibrating lateral restraint cantilever

Gellert, M.; Gluck, J.

doi:10.1016/0020-7403(72)90010-0

Cited by 11 publications

(9 citation statements)

References 2 publications

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“…In [12], closed-form solutions are presented for fundamental natural frequencies of non-homogeneous vibrating beams under axially distributed loads. The shape of the mode is postulated to coincide with the static deflection of the associated homogeneous beam without distributed axial load.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Clamped edge stress analysis in H-13 steel

Alejo

Miguel²,

Paredes-Rojas

et al. 2020

EEJET

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The dynamic behavior in the clamped edge stress of structures is not yet fully understood clearly; also, clamped structures involve uncertainty. This research presents a numerical and analytical study of clamped edge stress behavior due to the load imposed by the chip-cutting tool on a workpiece. Clamping system, which is made of H-13 steel and machining workpiece made of AISI 8620 steel are analyzed. The maximum clamped edge stress is analyzed through dynamic response, considering the machined part as a cantilever beam, involving the constitutive relations as well as the compatibility equations. The central differential equation of motion leads us to determine the modal stresses that are a primary characteristic of the structure and that are also distributed in it. Once the modal stress has been determined as well as the maximum amplitude at the free end of the specimen to be machined, it is possible to calculate the maximum clamped edge stress that is generated between both the specimen and the clamping system. Finally, a numerical analysis of the clamping jaw is performed for the discretised system and analyzed separately using the finite element method. Clamped edge stresses are assessed through a modal study using a set of numerical simulations to corroborate the modal stress estimated analytically. The results show that the clamped edge stress in the clamping system is a considerable influence in the design parameters of the structure. Therefore, complete knowledge of the dynamic response of the clamping system will lead to better structural design with the possibility of using different materials for the same purpose

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Clamped edge stress analysis in H-13 steel

Alejo

Miguel²,

Paredes-Rojas

et al. 2020

EEJET

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“…Jun et al [27] studied the coupled flexuraltorsional vibration of an axially loaded, thin walled beam with monosymmetrical cross sections and accounted for the effects of warping. The effect of axial load has also been previously studied by Murthy and Neogy [28] for clamped and pinned boundary conditions as well as by Gallert and Gluck [29] for the cantilevered boundary condition. Bokaian [30] studied the natural frequencies of a uniform single span beam subjected to a constant tensile axial load for various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

Jayasinghe¹

2021

Preprint

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Dynamic Finite Element (DFE) and conventional finite element formulations are developed to study the flexural - torsional vibration and stability of an isotropic, homogeneous and linearly elastic pre-loaded beam subjected to an axial load and end-moment. Various classical boundary conditions are considered. Elementary Euler - Bernoulli bending and St. Venant torsion beam theories were used as a starting point to develop the governing equations and the finite element solutions. The nonlinear Eigenvalue problem resulted from the DFE method was solved using a program code written in MATLAB and the natural frequencies and mode shapes of the system were determined form the Eigenvalues and Eigenvectors, respectively. Similarly, a linear Eigenvalue problem was formulated and solved using a MATLAB code for the conventional FEM method. The conventional FEM results were validated against those available in the literature and ANSYS simulations and the DFE results were compared with the FEM results. The results confirmed that tensile forces increased the natural frequencies, which indicates beam stiffening. On the contrary, compressive forces reduced the natural frequencies, suggesting a reduction in beam stiffness. Similarly, when an end-moment was applied the stiffness of the beam and the natural frequencies diminished. More importantly, when a force and end-moment were acting in combination, the results depended on the direction and magnitude of the axial force. Nevertheless, the stiffness of the beam is more sensitive to the changes in the magnitude and direction of the axial force compared to the moment. A buckling analysis of the beam was also carried out to determine the critical buckling end-moment and axial compressive force.

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“…Krishn et al [2], using Rayleigh-Ritz principle, introduced an iterative approximate solution method. Gellert and Gluck [3] investigated the effect of applied axial force on the lateral natural frequencies of a clamped-free beam with transverse restraint. Pilkington and Carr [4] introduced an approximate, noniterative solution for the frequencies of beams subjected to end moment and distributed axial force.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Finite Element Analysis of Bending-Torsion Coupled Beams Subjected to Combined Axial Load and End Moment

Kashani

Jayasinghe

Hashemi

2015

Shock and Vibration

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The dynamic analysis of prestressed, bending-torsion coupled beams is revisited. The axially loaded beam is assumed to be slender, isotropic, homogeneous, and linearly elastic, exhibiting coupled flexural-torsional displacement caused by the end moment. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the vibration and stability of such beams are explored. Using the closed-form solutions of the uncoupled portions of the governing equations as the basis functions of approximation space, the dynamic, frequency-dependent, interpolation functions are developed, which are then used in conjunction with the weighted residual method to develop the Dynamic Finite Element (DFE) of the system. Having implemented the DFE in a MATLAB-based code, the resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies of illustrative beam examples, subjected to various boundary and load conditions. The proposed method is validated against limited available experimental and analytical data, those obtained from an in-house conventional Finite Element Method (FEM) code and FEM-based commercial software (ANSYS). In comparison with FEM, the DFE exhibits higher convergence rates and in the absence of end moment it produces exact results. Buckling analysis is also carried out to determine the critical end moment and compressive force for various load combinations.

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The influence of axial load on eigen-frequencies of a vibrating lateral restraint cantilever

Cited by 11 publications

References 2 publications

Clamped edge stress analysis in H-13 steel

Clamped edge stress analysis in H-13 steel

Coupled flexural - torsional vibration and stability analysis of pre-loaded beams using conventional and dynamic finite element methods

Dynamic Finite Element Analysis of Bending-Torsion Coupled Beams Subjected to Combined Axial Load and End Moment

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