Journal ArticleDOI
Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach
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TLDR
In this paper, a size-dependent beam model is proposed for nonlinear free vibration of a functionally graded (FG) nanobeam with immovable ends based on the nonlocal strain gradient theory (NLSGT) and Euler-Bernoulli beam theory in conjunction with the von-Karman's geometric nonlinearity.About:
This article is published in International Journal of Engineering Science.The article was published on 2016-08-01. It has received 313 citations till now. The article focuses on the topics: Nonlinear system & Functionally graded material.read more
Citations
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Nonlocal elasticity in nanobeams: the stress-driven integral model
TL;DR: In this article, the bending field is placed in the proper position of input variable, giving to the elastic curvature field the role of output of the constitutive law, evaluated by convolution between the bending fields and an averaging kernel.
Journal ArticleDOI
Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material
TL;DR: In this article, the effects of the through-thickness power-law variation of a two-constituent functionally graded (FG) material and size-dependent parameters on nonlinear bending deflection and free vibration frequencies are investigated.
Journal ArticleDOI
Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory
TL;DR: In this paper, the bending, buckling and vibration problems of axially functionally graded (FG) beams are solved by a generalized differential quadrature method, and the influence of power-law variation and size-dependent parameters on the axially FG beam behavior is investigated.
Journal ArticleDOI
Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory
TL;DR: In this paper, the free vibration of nanobeams based on the non-local strain gradient theory was investigated and the results were compared with other beam models and other classical and non-classical theories.
Journal ArticleDOI
Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory
Li Li,Yujin Hu,Xiaobai Li +2 more
TL;DR: In this article, the longitudinal vibration analysis of small-scaled rods is studied in the framework of the nonlocal strain gradient theory and the equations of motion and boundary conditions are derived by employing the Hamilton principle.
References
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Journal ArticleDOI
Couple stress based strain gradient theory for elasticity
TL;DR: In this paper, an equilibrium relation is developed to govern the behavior of the couples, which constrained the couple stress tensor to be symmetric, and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system.
Journal ArticleDOI
Experiments and theory in strain gradient elasticity
TL;DR: In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors in small-scale structures and a strain gradient elastic bending theory for plane-strain beams is developed.
Journal ArticleDOI
Variational iteration method – a kind of non-linear analytical technique: some examples
TL;DR: In this paper, a variational iteration method for non-linear problems is proposed, where the problems are initially approximated with possible unknowns and a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Journal ArticleDOI
Nonlocal polar elastic continua
TL;DR: In this article, a continuum theory of non-local polar bodies is developed for nonlinear micromorphic elastic solids, and the balance laws and jump conditions are given.
Journal ArticleDOI
Second gradient of strain and surface-tension in linear elasticity
TL;DR: In this article, a linear theory of deformation of an elastic solid was formulated, in which the potential energy-density is a function of the strain and its first and second gradients.
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