Nonlinear resonant behaviors of bi-directional functionally graded material microbeams: One-/two-parameter bifurcation analyses

Chen, Xiaochao; Lü, Yixin; Zhu, Bin; Zhang, Xuanling; Li, Yinghui

doi:10.1016/j.compstruct.2019.110896

Cited by 30 publications

(4 citation statements)

References 68 publications

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“…As interpreted in this figure, the presented frequency-response curve is perfectly in tune with those given in Ref. [31]. In Figure 3, the convergence analysis of the reduced order model is executed when m x � m z � 1, f � 0.2, and c d � c r � 0.05.…”

Section: Resultssupporting

confidence: 77%

Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

Chen

et al. 2021

Shock and Vibration

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The nonlinear forced vibration of bidirectional functionally graded porous material beams where the material components gradient change in both thickness and axial directions are studied in this study. Combining von Karman’s geometric nonlinearity and first-order shear deformation theory, the governing equations describing the coupled deformations are formulated as a system of nonlinear partial differential equations. Utilizing the Galerkin method, the formulated continuous model is transformed to a coupled nonlinear ordinary differential dynamic system. By accomplishing bifurcation calculation for periodic response of the discrete system using pseudoarclength technique, the vibration response curves are obtained by extracting the max-min amplitude of periodic motions. To highlight the effect of nonlinearity, the linear and nonlinear dynamic responses of beam are demonstrated. It is found that the periodic motion of beam may undergo cyclic-fold bifurcation. Numerical results are presented to examine the effects of the system parameters, e.g., gradient indexes, porosity, damping coefficients, and aspect ratio.

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Section: Resultssupporting

confidence: 77%

Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

Chen

et al. 2021

Shock and Vibration

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“…e frequency-force-response curves and time histories are plotted to examine the effects of system parameters on the nonlinear parametric dynamics of beams. Unlike the primary resonance of BDFG beams [48] which is transversely excited and the resonance response which appears, when being near the linear fundamental frequency ω, the principal parametric resonance of an axially excited BDFG beam occurs, when the excitation frequency Ω is nearly double linear frequency (2ω l ). In Figure 3, the frequency-response curves for the transverse, longitudinal, and rotational motions of type I BDFG beam are plotted, when m � n � 1, L/h � 20, and c d � c r � 0.05.…”

Section: Shock and Vibrationmentioning

confidence: 99%

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

Lü¹,

Chen

2020

Shock and Vibration

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“…The moment Lyapunov exponent and perturbation methods were applied to analyze the stability of the double nanobeam. Other researchers studied several BDFG structures [22][23][24][25][26][27][28][29][30][31][32] and double-beam systems. [33][34][35][36] Based on the above discussion, it is noted that no efforts have been dedicated to carry out the free vibrations of bidirectional functionally graded (BDFG) double Euler-Bernoulli beams connected by a variable Winkler elastic layer, as they can represent applications as double-beam cranes, double-beam spectrometers, and double-beam interferometers.…”

Section: Introductionmentioning

confidence: 99%

Natural vibrations of double bi-directional functionally graded Euler–Bernoulli beams connected by a variable Winkler elastic layer

Sari

2022

Journal of Low Frequency Noise, Vibration and Active Control

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The free transverse vibrations of two-dimensional functionally graded double Euler–Bernoulli beam system connected through a variable Winkler elastic layer are presented. The Modulus of elasticity and the density of the material of the beams are assumed to vary along the thickness and the length of the beams according to power-law and exponential functions, respectively. The governing differential equations of motion are established by the means of Hamilton’s principle. The Chebyshev Spectral Collocation Method (CSCM) is used to calculate the natural frequencies of the two-dimensional functionally graded (2D-FG) double beams. The effects of several parameters such as the height ratio of the beams, the stiffness of the coupling layer, the axial and transverse functionally graded indexes, and the boundary conditions on the natural frequencies of the 2D-FG double beams have been investigated. The frequencies obtained from the CSCM have been validated by comparing them with those available in previous literature.

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Nonlinear resonant behaviors of bi-directional functionally graded material microbeams: One-/two-parameter bifurcation analyses

Cited by 30 publications

References 68 publications

Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

Nonlinear Parametric Dynamics of Bidirectional Functionally Graded Beams

Natural vibrations of double bi-directional functionally graded Euler–Bernoulli beams connected by a variable Winkler elastic layer

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