Nonlinear vibration analysis of an electrostatic functionally graded nano-resonator with surface effects based on nonlocal strain gradient theory

Esfahani, S.E.; Khadem, S.E.; Ebrahimi-Mamaghani, Ali

doi:10.1016/j.ijmecsci.2018.11.030

Cited by 84 publications

(23 citation statements)

References 53 publications

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“…Additionally, experimental studies have proven that classical continuum theories are incapable of predicting the mechanical behavior of the small-scale structures [35]. As a result, to capture the size effects of the material of nanosized structures, employing higher-order elasticity theories is essential in the mathematical modeling of these structures [36,37]. The nonlocal elasticity theory is one of the applicable non-classical theories that incorporate nanostructure-dependent size effects [38].…”

Section: Problem Formulationmentioning

confidence: 99%

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

et al. 2020

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In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

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Section: Problem Formulationmentioning

confidence: 99%

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

et al. 2020

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“…ϕ r (ξ)q r (τ) (16) in which q r , n, and ϕ r are dimensionless generalized coordinate, the number of basic functions, and acceptable mode shape for the transverse displacement of the system, respectively. The normalized mode shapes of a simply supported beam are given by [47]:…”

Section: Discretization Techniquementioning

confidence: 99%

Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

et al. 2020

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In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler-Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.

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“…According to Benjamin's formulation [4], in order to derive the partial differential equation of vibrational motion of the system, Hamilton's statement for an axially constrained pipe may be written as [63,64]:…”

Section: Theoretical Formulationsmentioning

confidence: 99%

On the dynamics of micro-tubes conveying fluid on various foundations

2019

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In this paper, using modified couple stress theory, dynamic stability of a cantilevered micro-tube embedded in several types of elastic media is studied. The governing equation for lateral vibrations of the micro-tube conveying fluid is derived using the extended Hamilton's principle. The numerical results are obtained by employing the extended Galerkin's method. For validation purposes, the obtained results for simple cases are compared and findings indicate a very good agreement with those available in the literature. The stability maps of different configurations with different flow velocities are studied and the influences of various parameters such as material length scale, external diameter and different elastic properties on the stability of the system are considered. Results indicate that elastic environments may enlarge the stability regions significantly at larger values of mass ratio parameter while decrease it for smaller values of mass ratio parameter. Moreover, using elastic media mathematically defined by series functions provides the capability to simulate almost any real time operational environment the micro-tube embedded in and results in an optimal stability state of the micro-structure carrying fluid flow.

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Nonlinear vibration analysis of an electrostatic functionally graded nano-resonator with surface effects based on nonlocal strain gradient theory

Cited by 84 publications

References 53 publications

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

On the dynamics of micro-tubes conveying fluid on various foundations

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