Resonant frequency tuning of nanobeams by piezoelectric nanowires under thermo‐electro‐magnetic field: a theoretical study

International Journal of Mechanical Sciences

2019

Self Cite

In this paper, a scale-dependent coupled nonlinear continuum-based model is developed for the mechanical behaviour of imperfect nanoscale tubes incorporating both the effect of the stress nonlocality and strain gradient effects. The scale effects on the nonlinear mechanics are taken into consideration employing a modified elasticity theory on the basis of a refined combination of Eringen's elasticity and the strain gradient theory. According to the Euler-Bernoulli theory of beams, the nonlocal strain gradient theory (NSGT) and Hamilton's principle, the potential energy, kinetic energy and the work performed by harmonic loads are formulated, and then the coupled scale-dependent equations of the imperfect nanotube are derived. Finally, Galerkin's scheme, as a discretisation technique, and the continuation method, as a solution procedure for ordinary differential equations, are used. The effects of geometrical imperfections in conjunction with other nanosystem parameters such as the nonlocal coefficient as well as the strain gradient coefficient on the coupled large-amplitude mechanical behaviour are explored and discussed.

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes

International Journal of Mechanical Sciences

2019

Self Cite

“…In general, the structural stiffness hardening is observed at microscale levels whereas the mechanics of nanostructures is usually governed by the stiffness softening. Therefore, size-dependent models including the couple stress [41][42][43][44][45][46][47][48][49][50][51] and strain gradient elasticities [52][53][54] are often used to analyse the mechanical behaviour of microstructures including microbeams, microbars and microplates while the nonlocal elasticity theory [55][56][57][58] is applied to nanoscale structures. However, to have a more general sizedependent continuum-based model capable of predicting size effects at different small scales, a combination of these modified elasticity theories [59] can be employed.…”

Section: Introductionmentioning

confidence: 99%

A review on the mechanics of nanostructures

International Journal of Engineering Science

2018

Self Cite

212

Understanding the mechanical behaviour of nanostructures is of great importance due to their applications in nanodevices such as in nanomechanical resonators, nanoscale mass sensors, electromechanical nanoactuators and nanogenerators. Due to the difficulties of performing accurate experimental measurements at nanoscales and the high computational costs associated with the molecular dynamics simulations, the continuum modelling of nanostructures has attracted a considerable amount of attention. Since size influences have a crucial role in the mechanics of structures at nanoscale levels, classical continuum-based theories have been modified to incorporate these effects. Among various modified continuum-based theories, the nonlocal elasticity and the nonlocal strain gradient elasticity have been employed to estimate the mechanical behaviour of nanostructures. In this review paper, first these two modified elasticity theories are briefly explained. Then, the nonlocal motion equations for different nanostructures including nanorods, nanorings, nanobeams, nanoplates and nanoshells are derived. Several papers which reported on the size-dependent mechanical behaviour of nanostructures using modified continuum models are reviewed. Furthermore, important results reported on the vibration, bending and buckling of nanostructures as well as the results of size-dependent wave propagation analyses are discussed.

“…In another paper, Murmu and Pradhan [30] examined thermo-mechanical oscillation of nanotubes resting on an elastic foundation. In addition, the mechanics of a system of carbon nanotubes and microtubules [31] as well as a system of 3 nanobeams and piezoelectric nanowires [32] were analysed using size-dependent beam models. Setoodeh et al [33] provided an exact solution for the nonlinear buckling of nanotubes with small-scale effects; they applied the nonlocal theory of beams to capture small-scale effects.…”

Section: Introductionmentioning

confidence: 99%

A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

2019

Microfluid Nanofluid

Self Cite

A coupled continuum model incorporating size influences and geometric nonlinearity is presented for the coupled motions of viscoelastic nonlinear nanotubes conveying nanofluid.A modified model of nanobeams incorporating nonlocal strain gradient effects is utilised for describing size influences on the bifurcation behaviour of the fluid-conveying nanotube. Furthermore, size influences on the nanofluid are taken into account via Beskok-Karniadakis theory. To model the geometric nonlinearity, nonlinear strain-displacement relations are employed. Utilising Hamilton's principle and the Kelvin-Voigt model, the coupled equations of nonlinear motions capturing the internal energy loss are derived. A Galerkin procedure with a high number of shape functions and a direct time-integration scheme are then employed to extract the bifurcation characteristics of the nanofluid-conveying nanotube with viscoelastic properties. A specific attention is paid to the chaotic response of the viscoelastic nanosystem. It is found that the coupled viscoelastic bifurcation behaviour is very sensitive to the flow velocity.