Flexoelectric effects on wave propagation responses of piezoelectric nanobeams via nonlocal strain gradient higher order beam model

Masoumi, Arian; Amiri, Ahad; Talebitooti, Roohollah

doi:10.1088/2053-1591/ab421b

Cited by 20 publications

(7 citation statements)

References 65 publications

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“…equal to the number of boundary conditions) and reorder as , so that R 1 becomes (47) where is square and non-singular. A suitable transformation is then , (48) which eliminates the boundary degrees of freedom since (49) The mass and stiffness matrices are then rearranged to match the ordering given in Eq. ( 47), and the transformed mass and stiffness matrices are and (50)…”

Section: Generalized Differential Quadrature Methodsmentioning

confidence: 99%

See 1 more Smart Citation

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

Rahmani

Faroughi

Friswell

2020

Mechanical Systems and Signal Processing

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A comprehensive vibrational analysis of bi-directional functionally graded (2D-FG) rotating nanobeams with porosities is studied for the first time. The beam is modeled based on general nonlocal theory (GNT) where the beam governing equations are derived depending on two different nonlocal parameters. Unlike Eringen's conventional form of nonlocal theory, the general nonlocal theory can reveal both hardening and softening behaviors of the material. Here, the attenuation functions are altered in both transverse and longitudinal directions of 2D-FG nanobeam. This feature, which has a significant effect on the vibrational characteristics, has not been considered in previous studies. Moreover, to estimate the effects of the higher-order transverse shear strains on the vibration of the nanobeam, Reddy's beam theory (RBT), which includes higher-order shear deformation, is employed. The material properties of the 2D-FG rotating nanobeam vary both in the length and thickness directions according to a power law.The generalized differential quadrature method (GDQM) is used to predict the vibration response. Also, the effects of material variation along the length and thickness directions, the rotating velocity of the nanobeam, the porosity volume fraction and the length to thickness ratio of the rotating nanobeam are illustrated and discussed in detail. The investigations performed in this study expose new phenomena for the vibration of nanobeams.

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Section: Generalized Differential Quadrature Methodsmentioning

confidence: 99%

“…The results show that using the TBT model reduces the accuracy and is the main reason that many researchers [46][47][48][49] have employed higher order beam theory to model nanobeams. Here, we considered the higher order beam theory in order to study comprehensive and more accurate vibration analysis.…”

Section: The Effects Ofmentioning

confidence: 99%

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

Rahmani

Faroughi

Friswell

2020

Mechanical Systems and Signal Processing

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“…The main deal of such investigations relies on free vibration, buckling, instability and wave dispersion analysis of the Nano-structures in the geometry of beam, plate and tube. 47–53 Among these works, Chen and Yan 54 performed preliminary research as a first attempt to make a bridge between the flexoelectricity phenomenon and pull-in instability behavior in smart Nano-switches. Their system was an electrostatically-actuated cantilever nanobeam sandwiched with a piezoelectric layer.…”

Section: Introductionmentioning

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:

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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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“…In their paper, the closed-form nonlinear frequency of the flexoelectric nanobeam was obtained. Masoumi et al [32] analyzed the flexoelectric effect on wave dispersion characteristics of piezoelectric nanobeams based on the nonlocal strain gradient theory. The static and dynamic mechanical behavior of flexoelectric nanobeams is significantly influenced by the nonlocal effect.…”

Section: Introductionmentioning

confidence: 99%

Electromechanical Analysis of Flexoelectric Nanosensors Based on Nonlocal Elasticity Theory

Zhou

2020

Micromachines

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Flexoelectric materials have played an increasingly vital role in nanoscale sensors, actuators, and energy harvesters due to their scaling effects. In this paper, the nonlocal effects on flexoelectric nanosensors are considered in order to investigate the coupling responses of beam structures. This nonlocal elasticity theory involves the nonlocal stress, which captures the effects of nonlocal and long-range interactions, as well as the strain gradient stress. Based on the electric Gibbs free energy, the governing equations and related boundary conditions are deduced via the generalized variational principle for flexoelectric nanobeams subjected to several typical external loads. The closed-form expressions of the deflection and induced electric potential (voltage) values of flexoelectric sensors are obtained. The numerical results show that the nonlocal effects have a considerable influence on the induced electric potential of flexoelectric sensors subjected to general transverse forces. Moreover, the induced electric potential values of flexoelectric sensors calculated by the nonlocal model may be smaller or larger than those calculated by the classical model, depending on the category of applied loads. The present research indicates that nonlocal effects should be considered in order to understand or design basic nano-electromechanical components subjected to various external loads.

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Flexoelectric effects on wave propagation responses of piezoelectric nanobeams via nonlocal strain gradient higher order beam model

Cited by 20 publications

References 65 publications

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

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

Electromechanical Analysis of Flexoelectric Nanosensors Based on Nonlocal Elasticity Theory

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