Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element

Le, Cong Ich; Le, Ngoc Anh Thi; Nguyen, Dinh Kien

doi:10.1016/j.compstruct.2020.113309

Cited by 37 publications

(4 citation statements)

References 52 publications

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“…are the matrices of the interpolating functions. The following linear and Hermite functions used in [17] are adopted for the functions N i (i = 1, 2) and H j (j = 1, . .…”

Section: Solution Methodsmentioning

confidence: 99%

Size-dependent behavior of a MEMS microbeam under electrostatic actuation

Tran

Lam

et al. 2022

Vietnam J. Mech.

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The size-dependent behavior of a silicon microbeam with an axial force in MEMS is studied using a nonlinear finite element procedure. Based on a refined third-order shear deformation theory and the modified couple stress theory (MCST), nonlinear differential equations of motion for the beam are derived from Hamilton’s principle, and they are transferred to a discretized form using a two-node beam element. Newton-Raphson based iterative procedure is used in conjunction with Newmark method to obtain the pull-in voltages and deflections of a clamped-clamped microbeam under electrostatic actuation. The influence of the axial force, applied voltage and material length scale parameter on the behavior of the beam is studied in detail and highlighted.

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“…are the matrices of the interpolating functions. The following linear and Hermite functions used in [17] are adopted for the functions N i (i = 1, 2) and H j (j = 1, . .…”

Section: Solution Methodsmentioning

confidence: 99%

Size-dependent behavior of a MEMS microbeam under electrostatic actuation

Tran

Lam

et al. 2022

Vietnam J. Mech.

Self Cite

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“…They verified results with the help of a numerical database, which was grounded on the Timoshenko beam formulation. Le et al 11 applied a third‐order shear deformation theory on 2D FG sandwich beams to analyze the free vibration and buckling response. The effective material properties were approximated using Voigt and Mori‐Tanaka models; the study highlighted the importance of micromechanical models.…”

Section: Introductionmentioning

confidence: 99%

Free vibration and buckling response of functionally graded triply periodic minimal surface beams considering neutral axis dislocation

Kurup,

Pitchaimani

2023

Noise & Vibration Worldwide

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The work pioneers a novel investigation into the free vibration and buckling behavior of triply periodic minimal surface beams, characterized by diverse distribution profiles. Using Euler-Bernoulli theory, under various boundary conditions, the investigation is carried out on four TPMS (Triply Periodic Minimal Surface) patterns, mainly gyroid, primitive, diamond and IWP (I-graph-wrapped package). The neutral axis would not coincide with the geometric center of the functionally graded beams so the neutral shift effect is taken into consideration appropriately. Governing differential equations are derived and the solutions are obtained numerically using the Ritz method. The mode shapes have also been calculated. It can be concluded that the type of pattern and distribution profile, boundary conditions, grade and neutral axis shift effect play a vital role in the prediction of vibration and buckling properties.

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“…Onedimensional or two-dimensional power functions described by one or two parameters are usually used as variation laws. In particular, a number of works study the behavior of inhomogeneous rods with properties that vary along one or two coordinates [14][15][16]. This is because rods remain one of the most common structural elements and are more accessible for full-scale experiments.…”

Section: Introductionmentioning

confidence: 99%

Efficient Numerical Methods of Inverse Coefficient Problem Solution for One Inhomogeneous Body

Vatulyan,

Uglich,

Dudarev

et al. 2023

Axioms

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In the present paper, the problems of longitudinal and flexural vibrations of an inhomogeneous rod are considered. The Young’s modulus and density are variable in longitudinal coordinate. Vibrations are caused by a load applied at the right end. The proposed method allows us to consider a wider class of inhomogeneity laws in comparison with other numerical solutions. Sensitivity analysis is carried out. A new inverse problem related to the simultaneous identification of the variation laws of Young’s modulus and density from amplitude–frequency data, which are measured in given frequency ranges, is considered. Its solution is based on an iterative process: at each step, a system of two Fredholm integral equations of the first kind with smooth kernels is solved numerically. The analysis of the kernels is carried out for different frequency values. To find the initial approximation, several approaches are proposed: a genetic algorithm, minimization of the residual functional on a compact set, and additional information about the values of the sought-for functions at the ends of the rod. The Tikhonov regularization and the LSQR method are proposed. Examples of reconstruction of monotonic and non-monotonic functions are presented.

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Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element

Cited by 37 publications

References 52 publications

Size-dependent behavior of a MEMS microbeam under electrostatic actuation

Size-dependent behavior of a MEMS microbeam under electrostatic actuation

Free vibration and buckling response of functionally graded triply periodic minimal surface beams considering neutral axis dislocation

Efficient Numerical Methods of Inverse Coefficient Problem Solution for One Inhomogeneous Body

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