Journal ArticleDOI
Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory
Omid Rahmani,O. Pedram +1 more
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In this article, the effects of the gradient index, length scale parameter and length-to-thickness ratio on the vibration of functionally graded material (FGM) nanobeams were examined.About:
This article is published in International Journal of Engineering Science.The article was published on 2014-04-01. It has received 282 citations till now. The article focuses on the topics: Timoshenko beam theory & Functionally graded material.read more
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Free vibration analysis of nonlocal strain gradient beams made of functionally graded material
Li Li,Xiaobai Li,Yujin Hu +2 more
TL;DR: In this article, a size-dependent Timoshenko beam model, which accounts for through-thickness power-law variation of a two-constituent functionally graded (FG) material, is derived in the framework of the nonlocal strain gradient theory.
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Bending of Euler–Bernoulli beams using Eringen’s integral formulation: A paradox resolved
TL;DR: In this article, the problem of static bending of Euler-Bernoulli beams using the Eringen integral constitutive equation is formulated, and a general method to solve the problem rigorously in integral form is proposed.
Journal ArticleDOI
Nonlinear free vibration of a functionally graded nanobeam using nonlocal strain gradient theory and a novel Hamiltonian approach
TL;DR: 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.
Journal ArticleDOI
A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates
TL;DR: In this article, wave propagation analysis of an inhomogeneous functionally graded (FG) nanoplate subjected to nonlinear thermal loading is investigated by the means of nonlocal strain gradient theory.
Journal ArticleDOI
A review of continuum mechanics models for size-dependent analysis of beams and plates
TL;DR: In this paper, a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures is presented, mainly focusing on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory.
References
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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.
Book
Nonlocal Continuum Field Theories
AC Eringen,JL Wegner +1 more
TL;DR: Memory-dependent nonlocal nonlocal Electromagnetic Elastic Solids as mentioned in this paper have been shown to be memory-dependent on nonlocal elasticity and nonlocal linear elasticity, as well as nonlocal Linear Elasticity and Nonlocal Fluid Dynamics.
Journal ArticleDOI
Size-dependent elastic properties of nanosized structural elements
Ronald E. Miller,Vijay B. Shenoy +1 more
TL;DR: In this article, a simple model is constructed to predict the size dependence of the effective stiffness of the structural element, and the important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulation of the bulk.
Journal ArticleDOI
Young’s modulus of single-walled nanotubes
A. Krishnan,Erik Dujardin,Thomas W. Ebbesen,Thomas W. Ebbesen,Peter N. Yianilos,Michael Treacy +5 more
TL;DR: In this paper, the stiffness of single-walled carbon nanotubes is estimated by observing their freestanding room-temperature vibrations in a transmission electron microscope, assuming that the vibration modes are driven stochastically and are those of a clamped cantilever.
Journal ArticleDOI
Nonlocal theories for bending, buckling and vibration of beams
J. N. Reddy,J. N. Reddy +1 more
TL;DR: In this article, the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories are reformulated using the nonlocal differential constitutive relations of Eringen.