Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory

Li, Li; Li, Xiaobai

doi:10.1016/j.ijmecsci.2016.06.011

Cited by 225 publications

(61 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The inhomogeneous rods are known to provide a suitable distribution of strength and weight for engineering structures [2]. A study of the vibration characteristics of these rods is a subject of considerable scientific interest that has wide applications in aerospace, civil and mechanical engineering [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Pillutla¹,

Sudheer²,

Yerikalapudy³

2018

J. vibroeng.

View full text Add to dashboard Cite

In this work, the problem of free longitudinal vibration of rods with variable cross-sectional area and material properties is investigated using the pseudospectral method. With the gradation of material properties like modulus of elasticity and mass density in the axial direction, the results corresponding to a functionally graded axial bar are obtained using the proposed pseudospectral formulation. The pseudospectral formulation used is relatively easy to implement and powerful in analyzing vibration problems. With the help of several numerical examples, the non-dimensional natural frequencies of rods obtained using the pseudospectral method are compared with those obtained by the analytical solution, generalized finite element method, the discrete singular convolution method and differential transformation method. The numerical results obtained show that the proposed technique allows boundary conditions to be incorporated easily and yields results with good accuracy and faster convergence rates than other methods.

show abstract

Section: Introductionmentioning

confidence: 99%

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Pillutla¹,

Sudheer²,

Yerikalapudy³

2018

J. vibroeng.

View full text Add to dashboard Cite

show abstract

“…The majority of size-dependent continuum models of nanorods have been developed via the nonlocal theory of elasticity. However, more recently, the NSGT has been employed for describing the longitudinal vibration [103] and tension [104] of nanorods; the modified rod model was successfully calibrated employing MD results. 11…”

Section: 1b Size-dependent Mechanics Of Nanorodsmentioning

confidence: 99%

A review on the mechanics of nanostructures

Farajpour

Ghayesh

Farokhi

2018

International Journal of Engineering Science

210

View full text Add to dashboard Cite

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.

show abstract

“…Hence, the solution of the differential equation (Equation 29) with the boundary conditions in Equations (30) and (31) provides the axial displacement…”

Section: Case I: Cf Fg Nano-rod With a Concentrated Load At The Free Endmentioning

confidence: 99%

“…Recently, the Eringen's integral law [1] has been combined with the strain gradient elasticity in [27] to formulate a higher-order nonlocal theory, thus collecting nonlocal theory and strain gradient theory into a single model. Using such a model, many contributions have been provided to model the size-dependent behavior of nano-rods and beams (see, e.g., [28][29][30][31][32][33][34][35]) and plates [36,37].…”

Section: Introductionmentioning

confidence: 99%

Modified Nonlocal Strain Gradient Elasticity for Nano-Rods and Application to Carbon Nanotubes

2019

View full text Add to dashboard Cite

Nowadays, the modified nonlocal strain gradient theory provides a mathematically well-posed and technically reliable methodology to assess scale effects in inflected nano-structures. Such an approach is extended in this paper to investigate the extensional behavior of nano-rods. The considered integral elasticity model, involving axial force and strain fields, is conveniently shown to be equivalent to a nonlocal differential problem equipped with constitutive boundary conditions. Unlike treatments in the literature, no higher-order boundary conditions are required to close the nonlocal problem. Closed-form solutions of elastic nano-rods under selected loadings and kinematic boundary conditions are provided. As an innovative implication, Young’s moduli of Single-Walled Carbon Nanotubes (SWCNT) weare assessed and compared with predictions of Molecular Dynamics (MD). New benchmarks for numerical analyses were also detected.

show abstract

Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory

Cited by 225 publications

References 55 publications

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

A review on the mechanics of nanostructures

Modified Nonlocal Strain Gradient Elasticity for Nano-Rods and Application to Carbon Nanotubes

Contact Info

Product

Resources

About