On the local/nonlocal piezoelectric nanobeams: Vibration, buckling, and energy harvesting

Naderi, Ali; Fakher, Mahmood; Hosseini-Hashemi, Shahrokh

doi:10.1016/j.ymssp.2020.107432

Cited by 46 publications

(12 citation statements)

References 87 publications

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“…So, only a few key values are selected and shown in Figure 3. As one of the key values for structural sti ness, it is shown that the de ection increases with the increase of internal characteristic scale parameter when the structural sti ness of the micro-beam is EI 10 −19 Nm 2 , or the exural rigidity gets weakening with the increase of the internal characteristic scale parameter, which is consistent with the basic assumptions of the nonlocal theory [17][18][19][20][21][22][23][24][25][26][27]. Nevertheless, if the structural sti ness is less than 10 −19 Nm 2 , the de ection decreases slightly that is not a reasonable phenomenon from the view of long-range interactions [17,18].…”

Section: Nonlocal Formulations Andsupporting

confidence: 78%

“…For example, the trend reverses when the structural sti ness is EI 8 × 10 −20 Nm 2 as compared with the case of EI 10 −19 Nm 2 . It implies a exural rigidity strengthening with the increase of the scale parameter, which is, however, inconsistent with the prediction of the nonlocal di erential constitutive model [19][20][21][22][23][24][25][26][27]. Hence, EI 8 × 10 −20 Nm 2 is not desirable in this example.…”

Section: Nonlocal Formulations Andcontrasting

confidence: 57%

“…Hence, the local cannot represent the original characteristics of the whole in the micro-/nano-scale, namely it is "nonlocality." e nonlocal theory has been applied extensively during the recent decades, of which almost all the research objects are micro-/nano-structures [19][20][21][22][23][24][25][26][27]. is is because the nonlocal theory contains the internal characteristic scale, and it is naturally suitable for the study of micro-/nano-mechanics.…”

Section: Introductionmentioning

confidence: 99%

“…As a widely concerned nonclassical continuum theory, Shaat et al [21] reviewed the recent advances in the nonlocal theory. Naderi et al [23] investigated the mechanics of piezoelectric nanobeams systematically including vibration, buckling, and energy harvesting using the classical and nonlocal theories, respectively. In addition to applications of the nonlocal theory, some scholars have developed new theoretical methods based on the Eringen's nonlocal theory.…”

Section: Introductionmentioning

confidence: 99%

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On Nonlocal Vertical and Horizontal Bending of a Micro-Beam

Zhu

Chen

Zhao

et al. 2022

Mathematical Problems in Engineering

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The vertical and horizontal bending of micro-beams subjected to axial compressive and transverse concentrated loadings is a common lateral deformation in micro-/nano-engineering that plays a significant role in the design and optimization of micro-/nano-devices. The present study aims to investigate it using the nonlocal theory. For this purpose, the simplified mathematical model is developed, and the nonlocal differential constitutive equation is applied. Since the mechanical properties of micro-beams are different from those of macro-beams, the non-classical nonlocal bending moment is introduced to improve the classical bending formulation in order to adapt to the vertical and horizontal bending of micro-beams. The effects of the external load, external size, structural stiffness, and internal characteristic scale on the vertical and horizontal bending deformation including the midpoint deflection and critical compression are presented. The present analytical model and results are validated by the finite element method. It is shown that the critical compression decreases with increasing the internal characteristic scale. Moreover, the midpoint deflection varies remarkably with respect to the axial and transverse loadings, structural stiffness, internal characteristic scale, and external size. An obvious nonlocal scale effect is found, in which the internal characteristic scale cannot be neglected compared with the external size. Besides, a threshold value of the structural stiffness is determined, and the connotation of the nonlocal interaction requires that the structural stiffness shall not be lower than that threshold. A mutual restriction between structural stiffness and external loadings is observed in the vertical and horizontal bending. In particular, it is further proved that the classical continuum mechanics can not be used in micro-/nano-scaled mechanics through a strange phenomenon that is contrary to mechanical common sense in the calculation example. The study is expected to be beneficial to the design and application of micro-beams subjected to the vertical and horizontal bending.

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Section: Nonlocal Formulations Andsupporting

confidence: 78%

Section: Nonlocal Formulations Andcontrasting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Nonlocal Vertical and Horizontal Bending of a Micro-Beam

Zhu

Chen

Zhao

et al. 2022

Mathematical Problems in Engineering

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“…All these forms with their enhanced versions are widely employed to model size-dependent behaviour of, especially nano and micro, structures with prominent neighbour relations (e.g. carbon nanotubes, graphene sheets, atomic chains/ arrays) (Polizzotto 2001;Ansari et al 2011;Rafii-Tabar et al 2016;Tuna and Kirca 2021;Tuna et al 2019;Eroglu 2020;Pisano et al 2021;Danesh et al 2021;Naderi et al 2021;Günay 2021). Nevertheless, their limitations must be acknowledged to avoid the improper practice leading to paradoxical results which are comprehensively reported in a current review article by Ceballes et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Topology optimization of scale-dependent non-local plates

Tuna

Trovalusci

2022

Struct Multidisc Optim

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The main objective of this work is to extend finite element-based topology optimization problem to the two-dimensional, size-dependent structures described using weakly non-local Cosserat (micropolar) and strongly non-local Eringen’s theories, the latter of which finds an application for the first time, to the best of Authors’ knowledge. The optimum material layouts that minimize the structural compliance are attained by means of Solid Isotropic Material with Penalization approach, while the desired smooth, mesh-independent, binary solutions are obtained using density filter accompanied by volume preserving Heaviside projection method. The algorithms are enhanced by including an element removal and reintroduction strategy to reduce the computational cost, and to prevent spurious excessive distortion of elements with very low density. Example problems of practical importance are investigated under the assumption of linear elasticity to validate the code and to clearly demonstrate the influence of internal length scales and different non-locality mechanisms on final configurations. Obtained macro-scale optimum topologies admit the characteristics of corresponding continuum theories, and appear to be in agreement with the mechanical response governed by particle interactions in micro/nanoscale.

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An investigation on the torsional vibration of a FG strain gradient nanotube

Uzun,

Yaylı,

Civalek

2024

Z Angew Math Mech

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In this work, an attention is paid to the prediction of torsional vibration frequencies of functionally graded porous nanotubes based on the Lam strain gradient elasticity theory. The nanotubes are formed of functionally graded porous nanomaterials that vary in the radial direction. This study also aims to obtain the analytical solution of the strain gradient model presented by Lam for torsional vibration response, in a simple manner, for different rigid or restrained boundary conditions. The torsion angle of a functionally graded nanotube is defined by an infinite Fourier series. Then, the Stokes’ transformation is applied to force the boundary conditions to the desired state. An eigenvalue problem is established with the help of the two systems of equations obtained. This eigenvalue problem, which includes deformable springs at both ends of the nanotube, appears as a general analytical solution that can find torsional vibration frequencies. It is shown that the vibrational responses can be significantly influenced by the through‐radius gradings of material, material length scale parameters and deformable springs of the functionally graded nanotubes and consequently can be predicted by giving proper values to torsional spring parameters.

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On the local/nonlocal piezoelectric nanobeams: Vibration, buckling, and energy harvesting

Cited by 46 publications

References 87 publications

On Nonlocal Vertical and Horizontal Bending of a Micro-Beam

On Nonlocal Vertical and Horizontal Bending of a Micro-Beam

Topology optimization of scale-dependent non-local plates

An investigation on the torsional vibration of a FG strain gradient nanotube

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