Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory

Khorshidi, Majid Akbarzadeh; Shariati, Mahmoud

doi:10.1007/s40430-015-0388-3

Cited by 32 publications

(3 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 6 illustrates the effect of number of nodes and the smoothing length value on the convergence of deflection response of a simply supported two-directional FG nanobeam with the following properties: k x = k z = 2, = 1 nm 2 , E ratio = 2. Numerical calculations are performed using uniformly distributed 9,15,17,19,21,23,25,27,41,81 and 121 nodes in the problem domain for three different values of smoothing length. According to the obtained results, the convergence rate is faster for h 0 = 1.2Δ.…”

Section: Results For Bending Analysismentioning

confidence: 99%

See 1 more Smart Citation

A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams

Rezaiee‐Pajand

Mokhtari

2019

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

Based on the Reddy-Bickford beam theory (RBBT), a comprehensive study on high-order bending, buckling and free vibration of two-directional functionally graded (FG) nanobeams is presented. The variation of the material properties is assumed to obey arbitrary power-law form in both axial and thickness directions. The equations of motion are derived using Hamilton's principle, and small-scale effects are captured by nonlocal elasticity theory of Eringen. The RBBT formulation leads to complicated governing equations, and 2D FGM introduces additional stiffness terms. Accordingly, the governing equations cannot be solved by classical analytical schemes, and thus, symmetric smoothed particle hydrodynamics (SSPH) meshless method is adopted as an efficient numerical solution approach. The revised super-Gauss function is used as the kernel function. To validate the developed SSPH code, benchmark problems are studied and the results are compared to the analytical solutions. In this context, excellent agreement is observed. Several numerical examples are included to illustrate the effects of gradient indexes, boundary conditions, size scale parameters, aspect and elastic modulus ratios on static and dynamic responses of two-directional FG nanobeams.

show abstract

Section: Results For Bending Analysismentioning

confidence: 99%

“…In a recent paper by Ebrahimi and Barati, analytical solutions were obtained for free vibration of FG nanobeams based on the Reddy-Bickford beam theory [31]. Further studies addressing the behavior of ordinary and FG nanobeams can be found in [32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams

Rezaiee‐Pajand

Mokhtari

2019

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

show abstract

“…Since then, many investigations have been conducted to compute the Casimir attraction for different geometries including parallel plates [16][17][18], plate-sphere [19], parallel cylinders [20] and plate-cylinder [21]. Several investigations have investigated the instability characteristics and nonlinear analysis of micro/nano-scale structures by employing different assumptions and theories such as nonlocal elasticity [22][23][24] modified couple stress theory [25][26][27][28], strain gradient theory [29,30], modified strain gradient theory [31], strain-inertia gradient elasticity [32], etc. A nano-scale device might adhere to its substrate due to Casimir force if the minimum gap between the flexible beam and the substrate is not considered.…”

mentioning

confidence: 99%

Nonlinear vibration and adhesion instability of Casimir-induced nonlocal nanowires with the consideration of surface energy

Sedighi

Bozorgmehri

2016

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

Because of excellent physical properties of nanowire-based nano-structures, e.g. small size with large ratio of surfacearea to volume, the applications of these structures are growing rapidly. Nanowires are of great interest for detecting nano-objects with high sensitivity and also have noticeable applications in several industries such as optics [1], nanoelectromechanical systems (NEMS) [2], biological or gas sensing devices [3], flexible electronics and renewable energy technologies [4], ultrasensitive biological and chemical sensors [5], pH measurements [6], resonators and actuators [7, 8] and multifunctional NEMS. When the electronic and mechanical systems are fabricated at nano-scale size, some new phenomena that originated from the nano-size quantum effects have become more important and the motion of nanowire-based structure is affected by the small-scale quantum electrodynamic interactions such as vacuum fluctuations. The effect of vacuum fluctuation forces is usually modeled through the Casimir attraction which is the dominant phenomenon in sub-micron separations [9]. By integrating a force-sensing micromechanical beam and an electrostatic actuator on a single chip, Zou et al. [10] demonstrated the Casimir effect between two micromachined silicon components on the same substrate. Lombardo et al. [11] numerically evaluate the Casimir interaction energy for configurations involving two perfectly conducting eccentric cylinders and a cylinder in front of a plane. Emig et al. [12] found the exact Casimir force between a plate and a cylinder by assuming an intermediate geometry between parallel plates and the plate-sphere. Tercas et al. [13] considered the mechanical coupling between a two-dimensional Bose-Einstein condensate and a graphene sheet via the vacuum fluctuations Abstract The following research work deals with the size-dependent dynamic instability of suspended nanowires in the presence of Casimir force and surface effects. Specifically, the Casimir-induced instability of nanostructures with circular cross-section and cylinder-plate geometry is studied. Following the Gurtin-Murdoch model and nonlocal elasticity, the governing equation of motion for nanowires is derived. To express the Casimir attraction of cylinder-plate geometry, two approaches, e.g. proximity force approximation (PFA) for small separations and Dirichlet asymptotic approximation for large separations are studied. To overcome the difficulties for solving a nonlinear problem, a step-by-step numerical method is utilized. The effects of nonlocal parameter, surface energy and vacuum fluctuations on the dynamic instability characteristic and adhesion time of nanowires are studied. It is observed that the phase portrait of Casimir-induced nanowires exhibit periodic and homoclinic orbits.

show abstract

Nanostructure‐dependent dispersion of carbon nanostructures: New insights into the modified couple stress theory

Khorshidi

Soltani

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper presents a size‐dependent analysis of carbon nanostructures to put forward some new insights into the conventional modified couple stress theory. In fact, a micro‐inertia length scale parameter is added to the equation of motion to compensate the deficiency of the theory in describing the size effect of the longitudinal dispersion. In this study, the longitudinal dispersions of carbon nanotubes, graphene, and graphite layers are investigated to obtain the micro‐inertia length scale parameter, and the flexural dispersions of carbon nanotubes and graphene layer are assessed to expose the size dependency of the couple‐stress length scale parameter. The results indicate that the micro‐inertia length scale parameter can directly be related to the lattice size, while the couple‐stress length scale parameter depends on some more factors like geometry, size, and material properties. Finally, some general relations are proposed for the first time to make a connection between these two distinct parameters and other features.

show abstract

Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory

Cited by 32 publications

References 44 publications

A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams

A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams

Nonlinear vibration and adhesion instability of Casimir-induced nonlocal nanowires with the consideration of surface energy

Nanostructure‐dependent dispersion of carbon nanostructures: New insights into the modified couple stress theory

Contact Info

Product

Resources

About