Flexoelectric effect on vibration responses of piezoelectric nanobeams embedded in viscoelastic medium based on nonlocal elasticity theory

Zhang, D. P.; Lei, Yiyan; Adhikari, Sondipon

doi:10.1007/s00707-018-2116-4

Cited by 45 publications

(9 citation statements)

References 22 publications

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“…Constitutive relations for piezoelectric materials with accordance to the higher order polarization effect (flexoelectricity) are as following: 56 in which σxx, τxxz, Dz and Qzz express the stress, higher order stress, electric displacement and electric quadrupole, respectively. Also, C11, e31, μ31, K33 and b33 denote respectively the elastic constant, piezoelectric coefficient, flexoelectric coefficient, dielectric constant and electrical coupling coefficient.…”

Section: System Description and Mathematical Formulationmentioning

confidence: 99%

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Nonlinear static pull-in instability analysis of smart nano-switch considering flexoelectric and surface effects via DQM

Masoumi

Amiri

Vesal

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper deals with the investigation of nonlinear static pull-in instability of smart Nano-switches regarding the new size-dependent phenomenon, known as flexoelectricity, together with the surface effects. It is noteworthy that the coupling effect of the flexoelectricity and surface elasticity on nonlinear static pull-in instability of electrostatically-actuated Nano-switches has not been studied before. Euler-Bernoulli beam assumptions in conjunction with the von-Karman nonlinearity are considered to formulate the problem. The Nano-switch is subjected to electrostatic actuation force with fringing field effect as well as Casimir force. Refined constitutive relations for piezoelectric materials capturing the flexoelectric effects are taken into consideration for mathematical modeling. Additionally, a surface elasticity approach is employed to reach an accurate model for the system. Considering the imposed electric boundary conditions, Gauss’s equation is solved to acquire the electric potential distribution along with the thickness of the Nano-switch. Thereafter, Hamilton’s principle is hired to derive the coupled nonlinear governing equations of the system. Utilizing the differential quadrature method (DQM), the nonlinear ordinary differential equations are transformed into a system of nonlinear algebraic equations. Consequently, Newton-Raphson method is exploited as a numerical method to solve the obtained algebraic equations which leads to the pull-in voltage. Investigating the maximum displacement of the Nano-switch in response to the applied electrostatic force, the effects of various involved parameters such as flexoelectricity and surface elasticity on pull-in instability are explored in detail. Furthermore, the size-dependent behavior of the pull-in instability against the flexoelectric, surface effects and applied piezoelectric voltage is analyzed. Totally, it is revealed that the flexoelectricity may exhibit a substantial influence on the pull-in behavior of smart Nano-switches, especially for some cases with small thicknesses. Therefore, this effect should be taken into account to reach an accurate, reliable and optimized design for Nano-switches.

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Section: System Description and Mathematical Formulationmentioning

confidence: 99%

“…Furthermore, according to Gauss’s law, an equation is written between the scalar electric potential and the electric displacement as follows: 56 …”

Section: System Description and Mathematical Formulationmentioning

confidence: 99%

Nonlinear static pull-in instability analysis of smart nano-switch considering flexoelectric and surface effects via DQM

Masoumi

Amiri

Vesal

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Eringen [31] converted the nonlocal model from integral form into a so-called equivalent differential form due to the difficulty to solve the integro-differential equations. The nonlocal differential model is widely applied to capture the softening effect of micro-and nano-scale structures, for example, [32][33][34]. However, several studies show that size-dependent response does not appear for a tensile bar [35], and static bending of Euler-Bernoulli and Timoshenko beams with a concentrate force at the free end [36,37].…”

Section: Introductionmentioning

confidence: 99%

Elastic buckling and free vibration of nonlocal strain gradient Euler‐Bernoulli beams using Laplace transform

Bian

Qing

2021

Z Angew Math Mech

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Previous studies have shown that Lim's nonlocal strain gradient differential model would lead to some inconsistencies for the static bending of Bernoulli-Euler and Timoshenko beams, though it is widely applied to address both softening and toughening size-effect. In this work, nonlocal strain gradient integral model is applied to study the elastic buckling and free vibration of Bernoulli-Euler beam under different boundary conditions. The differential governing equation and corresponding boundary conditions are derived via the Hamilton's principle, and the relation between strain and nonlocal stress is expressed in integral form. The Laplace transform technique is applied to solve the integro-differential equations directly, and the explicit expression for bending deflections and moments is obtained with six unknown constants. The nonlinear characteristic equations to determine the characteristic buckling load and vibration frequency are derived explicitly in consideration of corresponding boundary conditions. The buckling load and vibration frequency from present model are validated against to the existed results in literature. Consistent softening and toughening responses respect to length-scale parameters can be obtained for both elastic buckling and free vibration.

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“…Smart materials such as piezoelectric [15], flexoelectric [16] and shape memory alloy (SMA) [17] have been widely and successfully applied in MEMS to realise the special functions for decades. The Young's modulus of shape memory materials can be changed under the thermal field or light field.…”

Section: Introductionmentioning

confidence: 99%

Pull‐in analysis of microbeam laminated with LASMP

Guo

Yang

Zhai

2020

Micro & Nano Letters

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This work focuses on the pull-in phenomena of electrically actuated size-dependent microbeam laminated with the light-activated shape memory polymer, which can realise the Young's modulus variation under the light exposure. Based on the modified couple stress theory, a size-dependent microbeam model is developed. The dynamic governing equation of the microbeam is derived according to the Hamilton principle and solved by the Galerkin method and Runge-Kutta method numerically. The reliability and accuracy of the present method are validated experimentally. The static and dynamic pull-in behaviours of the microbeam are studied when the microbeam is under a purely direct current voltage and alternating current voltage, respectively. Influences of the size effect and dynamic Young's modulus on pull-in behaviour of the microbeam are discussed comprehensively. This research may be helpful and useful in electrostatically actuated microstructure applications and provide a theoretical foundation for designers and engineers.

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Flexoelectric effect on vibration responses of piezoelectric nanobeams embedded in viscoelastic medium based on nonlocal elasticity theory

Cited by 45 publications

References 22 publications

Nonlinear static pull-in instability analysis of smart nano-switch considering flexoelectric and surface effects via DQM

Nonlinear static pull-in instability analysis of smart nano-switch considering flexoelectric and surface effects via DQM

Elastic buckling and free vibration of nonlocal strain gradient Euler‐Bernoulli beams using Laplace transform

Pull‐in analysis of microbeam laminated with LASMP

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