Parametric studies on bending vibration of axially-loaded twisted Timoshenko beams with locally distributed Kelvin–Voigt damping

Chen, Wei‐Ren

doi:10.1016/j.ijmecsci.2014.07.006

Cited by 20 publications

(6 citation statements)

References 46 publications

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“…Further, an essential hypothesis that the lateral displacement z T is identical within the entire cross-section should be mentioned to validate the further damping model Zhang et al., 2017). Hence, by applying the specific K-V damping model (Zhao et al., 2005; Chen, 2014), the general damping effects due to the structural deformations can be evaluated by where σ and ε denote the stretching stress and the strain flow within the beam, and τ describes the shear stress. C b and C s are the notations of viscous damping coefficients related to inner stretching and shearing motions respectively.…”

Section: Modeling Of the Governing Equationsmentioning

confidence: 99%

“…Aiming to validate the L-method, such particular treatment is primarily mathematical reasonable, so the complex domain derivations is avoided successfully. In fact, Chen (2014) set C b and C s to identical values in actual computations and analyses. Capsoni et al.…”

Section: Fundamental Solutions Under Impact Loadmentioning

confidence: 99%

“…(2015) utilized complex mode theory and accounted for the proportional Rayleigh damping model ultimately to perform possible numerical experiments. The finite element method (FEM) was used by Chen (2014) to analyze the impacts of the twist angle on inherent frequency, where the K-V damping effect was considered, whereas the explicit modal shapes and corresponding dynamic responses were not worked out. Liu et al.…”

Section: Introductionmentioning

confidence: 99%

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Fundamental solution and its validation by numerical inverse Laplace transformation and FEM for a damped Timoshenko beam subjected to impact and moving loads

Zhang

Liang

Zhao

2018

Journal of Vibration and Control

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This paper, taking the clamped boundary condition as an example, develops Su and Ma's fundamental solutions of the dynamic responses of a Timoshenko beam subjected to impact load. Based on that, a further extension regarding the general moving load case is also established. Kelvin–Voigt damping, whether proportionally or nonproportionally damped, is incorporated into the model, making it more comprehensive than the model of Su and Ma. Numerical inverse Laplace transformation is introduced to obtain the time-domain solution, where Durbin's formula and the corresponding convergence criteria are utilized in numerical experiments. Further, the real modal superposition method is applied at an analytical level to validate the numerical results by applying a proportionally damped condition. Total comparisons are made between the methods by sufficient case studies. The dynamic responses with and without damping effect are computed with wider slenderness to verify the correctness and effectiveness of the numerical results. Furthermore, parametric studies regarding the damping coefficients are performed to explore the nonproportional damping effect. The results show that the structural damping has significant influences on the dynamic behaviors and is especially stronger at small slender ratios. As the damping decreases the inherent frequencies and excites the low-frequency modal components more actively, a resonant phenomenon appears in high slenderness case when the beam experiences a low-speed moving load. Additionally, the computations in the moving load case indicate that the algorithm convergence is preferable when the number of grids exceeds 1000.

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Section: Modeling Of the Governing Equationsmentioning

confidence: 99%

Section: Fundamental Solutions Under Impact Loadmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fundamental solution and its validation by numerical inverse Laplace transformation and FEM for a damped Timoshenko beam subjected to impact and moving loads

Zhang

Liang

Zhao

2018

Journal of Vibration and Control

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“…The first approach is used for slender rods (straight lines or planes normal to the neutral beam axis remain straight and normal after deformation) [5][6][7][8] and the latter for stocky rods (the rods with small length-to-depth ratio) in which the transverse shear deformation and the rotatory inertia are involved [9,10]. Various aspects for Timoshenko beam theory have been investigated, for example, beams with asymmetric cross-section [11], beams excited by a sequence of moving masses [12], twisted beams [13,14], beams with damping [14] and beams under tangential follower forces [15][16][17]. The Timoshenko beam theory can also be used to study dynamic stability of sandwich beams [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods

Obara

Gilewski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The objective of this paper is to determine dynamic instability areas of moderately thick beams and frames. The effect of moderate thickness on resonance frequencies is considered, with transverse shear deformation and rotatory inertia taken into account. These relationships are investigated using the Timoshenko beam theory. Two methods, the harmonic balance method (HBM) and the perturbation method (PM) are used for analysis. This study also examines the influence of linear dumping on induced parametric vibration. Symbolic calculations are performed in the Mathematica programme environment. The majority of studies reported in the literature use numerical analysis for determining resonance areas. Only a few researchers have adopted an analytical approach.The purpose of this article is to propose two methods for determining parametric resonance areas for moderately thick beams and frames under various support conditions. These methods, never before used for this purpose, are the harmonic balance method (HBM) and the perturbation method (PM). The latter of these two methods represents a surprisingly simple tool for achieving the goal, as its results are very close to those obtained from the standard harmonic balance method which is far more troublesome in application.An analytical approach is used to analyze simply supported moderately thick beams, and a numerical technique, based on the finite element method with the use of physical shape functions [32] is applied to other beams and frames. The analysis covers the effect of moderate thickness on resonance frequencies and the influence of type of fixing used in the beams and frames on the instability areas. For this purpose, shear deformation and rotatory inertia are taken into account. The Timoshenko beam theory is applied to examine how these factors affect resonance frequency values. The results are compared with those obtained with the Bernoulli-Euler beam theory.In addition, the effect of linear dumping of induced parametric vibration is considered. Analysis of a simply supported beamThe following assumptions are adopted in physical and numerical modeling:• The beam is made of an isotropic homogenous linear elastic material with Young's modulus E, shear modulus G and Poisson's ratio v.

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“…The dynamic stability of a spinning twisted Timoshenko beam under a periodic compressive axial load was analyzed by Chen [42] to examine the effects of twist angle, spinning speed, static axial load, geometric aspects and boundary conditions on the instability regions. Bending vibrations of an axially loaded twisted Timoshenko beam with locally distributed Kelvin-Voigt damping were presented by Chen [43] to study the effects of the twist angle, damping amount, size and location of damped segment, axial load and restraint types on the eigenfrequency of the damped twisted beams.…”

Section: Introductionmentioning

confidence: 99%

Parametric instability of twisted Timoshenko beams with localized damage

Chen

2015

International Journal of Mechanical Sciences

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Parametric studies on bending vibration of axially-loaded twisted Timoshenko beams with locally distributed Kelvin–Voigt damping

Cited by 20 publications

References 46 publications

Fundamental solution and its validation by numerical inverse Laplace transformation and FEM for a damped Timoshenko beam subjected to impact and moving loads

Fundamental solution and its validation by numerical inverse Laplace transformation and FEM for a damped Timoshenko beam subjected to impact and moving loads

Dynamic stability of moderately thick beams and frames with the use of harmonic balance and perturbation methods

Parametric instability of twisted Timoshenko beams with localized damage

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