Vibrations of Nonlocal Timoshenko Beams using Orthogonal Collocation Method

Wu, Lai‐Yun; Chung, Lap-Loi; Wu, Ching‐Yuan; Huang, Hsu-Hui; Lin, Kun-Wei

doi:10.1016/j.proeng.2011.07.301

Cited by 3 publications

(3 citation statements)

References 2 publications

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“…Two dimensional mass, μ r , and frequency, f r , ratio are introduced to standardise the structure-damper system (Elias and Matsagar 2018;Salvi et al 2018): where f d is the mass damper frequency (= 1/T d ) and Ω s,j = Ω s,1 ,…,Ω s,n (= 1/T s,1 , …, 1/T s,n ) is the selected modal frequency of the structure corresponding to the mode j. A possible criterium to distribute the damper masses on the structure is carrying out the modal analysis (Elias and Matsagar 2018;Wu et al 2011).…”

Section: Methodsmentioning

confidence: 99%

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Zacchei

Brasil

2023

Arab J Geosci

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Anti-seismic devices are employed to implement the best performance of the structures under earthquakes. In this paper, semi-active tuned mass dampers (SA-TMDs) are studied by considering several combinations of variable friction forces and external disturbances. The variable damping model is used, where the goal consists in estimating the external actions to find the best friction force for system dampening. In particular, general, sinusoidal, and Gaussian dynamic loadings are considered. To obtain the response of the structure and dampers, several numerical solutions have been implemented. Probabilistic and determines analyses have been also developed to study different damper characteristics. Results show that a SA-TMD can reduce the structure displacements up to ~ 70.0% indicating a good performance in controlling different oscillations. This technology not only preserves the integrity of a structure mitigating its vibrations but also improves the life of occupants and their safety and comfort. This is beneficial from the perspective of practical application, and it is an advancement with respect to this theme.

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Section: Methodsmentioning

confidence: 99%

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Zacchei

Brasil

2023

Arab J Geosci

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“…Also, by applying PDQM to equations (3,4), (5)(6)(7)(8)(9)(10) and (12), one can reduce the problem to the following linear algebraic system:…”

Section: Solution Of Timoshenko Problemmentioning

confidence: 99%

“…Behera [9] studied free vibration of Euler and Timoshenko nanobeams using boundary characteristic orthogonal polynomials. In [10] the orthogonal collocation method is applied to study the free vibrations of nonlocal Timoshenko beams by using piecewise cubic Hermite polynomials. Eltaher [11] studied the vibration analysis of Euler-Bernoulli nanobeams using finite element method.…”

Section: Introductionmentioning

confidence: 99%

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Elkhalek¹,

Osman²,

Matbuly³

2019

ENGMATH

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This work concerns with free vibration analysis of cracked nanobeam problems. Based on Eringen's nonlocal elasticity theory, the governing equation of Euler-Bernoulli and Timoshenko nanobeams, are derived. It is assumed that strain at a certain point is a function of the strains at all points within the influence domain. The cracked beam is modeled as multisegments connected by a rotational spring located at the cracked sections. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. Polynomial based differential quadrature method is employed to solve the problem. Derivatives of the field quantities are approximated as a weighted linear sum of the nodal values. For different supporting cases, the boundary conditions are directly substituted in the equation of motion, such that the problem is reduced to that of linear homogeneous algebraic system. This suggested numerical scheme accurately determined angular frequencies of the problem. A comparative study is tabulated to compare the obtained results with the previous ones. Further, a parametric study is introduced to investigate the influence of crack locations, crack severity and the nonlocal scale parameter on the obtained results. The obtained results recorded that frequency values decrease with the increasing of both of crack severity and the nonlocal scale parameter. The results of the proposed scheme may be applied for structural health monitoring.

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Study on the effect of small scale on the wave reflection in carbon nanotubes using nonlocal Timoshenko beam theory and wave propagation approach

Bahrami

Teimourian

2016

Composites Part B: Engineering

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Vibrations of Nonlocal Timoshenko Beams using Orthogonal Collocation Method

Cited by 3 publications

References 2 publications

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Semi-active tuned mass dampers under combined variable actions of friction forces and external disturbances

Vibrations Analysis of Cracked Nanobeams Using Quadrature Technique

Study on the effect of small scale on the wave reflection in carbon nanotubes using nonlocal Timoshenko beam theory and wave propagation approach

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