Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Nguyen, Dinh Kien; Bui, Van Tuyen

doi:10.1155/2017/7025750

Cited by 14 publications

(7 citation statements)

References 36 publications

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“…The beam element formulated from the linear interpolation, however encounters the shear-locking problem [25]. To avoid the shear-locking problem, the displacements and rotation are interpolated from their nodal values by using the hierarchical functions as follows [26]…”

Section: Finite Element Formulationmentioning

confidence: 99%

Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element

Nguyen²

2022

Vietnam J. Mech.

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In this paper, vibration of Timoshenko microbeams with an axial force in micro-electromechanical systems (MEMS) is studied for the first time by using a nonlinear finite element procedure. Based on the von Kármán geometric nonlinearity and the modified couple stress theory (MCST), a beam element is formulated by employing hierarchical functions to interpolate the displacement field. Using the derived element, the discretized equation of motion for the microbeam is constructed and then solved by the Newton-Raphson iterative procedure in conjunction with the Newmark method. The natural frequencies, pull-in voltages and dynamic deflections are computed for a clamped-clamped microbeam under electrostatic actuation of a given direct current (DC) voltage. The numerical result reveals that the axial force and the microsize effect have a significant influence on the vibration, and the fundamental frequency of the microbeams is underestimated by ignoring the size effect. The effects of the axial force, the applied voltage and the material length scale parameter on the vibration of the beam are studied in detail and highlighted.

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Section: Finite Element Formulationmentioning

confidence: 99%

Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element

Nguyen²

2022

Vietnam J. Mech.

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“…e differential equation of motion for the beam can be obtained by applying Hamilton's principle to (8), (11), and (14). However, due to the rigidities and mass moments, as seen from (10) and (13), functions of x, a closed-form solution for such equation is difficult to obtain.…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…e effect of axial compressive force and the temperature rise were taken into consideration by the authors. Nguyen and Bui [14] studied the effect of temperature rise on dynamic response of a FGM Timoshenko beam under a moving load using a hierarchical beam element. Finite element method was also used by Esen et al [15] in computing the dynamic response of a FGM Timoshenko to an accelerating moving mass.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Behavior of a Bidirectional Functionally Graded Sandwich Beam under Nonuniform Motion of a Moving Load

Nguyen¹,

Le³

et al. 2020

Shock and Vibration

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A bidirectional functionally graded Sandwich (BFGSW) beam model made from three distinct materials is proposed and its dynamic behavior due to nonuniform motion of a moving point load is investigated for the first time. The beam consists of three layers, a homogeneous core, and two functionally graded face sheets with material properties varying in both the thickness and longitudinal directions by power gradation laws. Based on the first-order shear deformation beam theory, a finite beam element is derived and employed in computing dynamic response of the beam. The element which used the shear correction factor is simple with the stiffness and mass matrices evaluated analytically. The numerical result reveals that the material distribution plays an important role in the dynamic response of the beam, and the beam can be designed to meet the desired dynamic magnification factor by appropriately choosing the material grading indexes. A parametric study is carried out to highlight the effects of the material distribution, the beam layer thickness and aspect ratios, and the moving load speed on the dynamic characteristics. The influence of acceleration and deceleration of the moving load on the dynamic behavior of the beam is also examined and highlighted.

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“…Vibration of an FGM Euler-Bernoulli beam due to a moving oscillator was investigated in [14] by the Runge-Kutta method. Finite element method has been also used to study vibration of FGM beams excited by moving loads [15,16].…”

Section: Introductionmentioning

confidence: 99%

Vibration of FGSW Beams Under Nonuniform Motion of Moving Load Using an Efficient Third-Order Shear Deformation Finite Element Formulation

Le¹,

Nguyen²

2020

JST

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Vibration of functionally graded sandwich (FGSW) beams under nonuniform motion of a moving load is studied using a third-order shear deformation finite element formulation. The beams consists three layers, a homogeneous ceramic core and two functionally graded faces. Instead of the rotation, the finite element formulation is derived by using the transverse shear rotation as a unknown. Newmark method is used to compute the dynamic response of the beams. Numerical result reveals that the derived formulation is efficient, and it is capable to give accurate vibration characteristics by a small number of the elements. A parametric study is carried out to illustrate the effects of the material distribution, layer thickness ratio and moving load speed on the dynamic behavior of the beams. The influence of acceleration and deceleration of the moving load on the vibration of the beams is also examined and discussed.

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Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher‐Order Hierarchical Beam Element

Cited by 14 publications

References 36 publications

Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element

Vibration of electrically actuated MEMS Timoshenko microbeams based on a hierarchical beam element

Dynamic Behavior of a Bidirectional Functionally Graded Sandwich Beam under Nonuniform Motion of a Moving Load

Vibration of FGSW Beams Under Nonuniform Motion of Moving Load Using an Efficient Third-Order Shear Deformation Finite Element Formulation

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