Journal ArticleDOI
Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen's theory using differential quadrature method
Majid Ghadiri,Navvab Shafiei +1 more
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TLDR
In this article, the effect of nonlinear small-scale, angular speed, hub radius and nonlinear amplitude of rotary nanobeam on the bending vibration of a rotating cantilever was investigated.Abstract:
This study investigates the small scale effect on the nonlinear bending vibration of a rotating cantilever and propped cantilever nanobeam. The nanobeam is modeled as an Euler---Bernoulli beam theory with von Karman geometric nonlinearity. The axial forces are also included in the model as the true spatial variation due to the rotation. Hamilton's principle is used to derive the governing equation and boundary conditions for the Euler---Bernoulli beam based on Eringen's nonlocal elasticity theory. The differential quadrature method as an efficient and accurate numerical tool in conjunction with a direct iterative method is adopted to obtain the nonlinear vibration frequencies of nanobeam. The effect of nonlocal small---scale, angular speed, hub radius and nonlinear amplitude of rotary nanobeam is discussed.read more
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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
Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects
TL;DR: In this article, a size-dependent Euler-Bernoulli beam model is proposed to investigate the scaling effect on the post-buckling behaviors of functionally graded (FG) nanobeams with the von Karman geometric nonlinearity.
Journal ArticleDOI
Nonlinear vibration of axially functionally graded tapered microbeams
TL;DR: In this article, the size-dependent vibration of a non-uniform axially functionally graded (AFG) microbeam is studied and the results can be used in designation of many microstructures such as micro electro mechanical systems (MEMS), micro-actuators, etc.
Journal ArticleDOI
Twisting statics of functionally graded nanotubes using Eringen’s nonlocal integral model
Xiaowu Zhu,Li Li +1 more
TL;DR: In this article, a nonlocal integral model is formulated to investigate the twisting static behaviors of through-radius functionally graded (FG) nanotubes based on Eringen's non-local integral elasticity.
Journal ArticleDOI
On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams
TL;DR: In this paper, the size dependent nonlinear vibration behavior of imperfect uniform and non-uniform functionally graded (FG) microbeams is investigated based on modified couple stress and Euler-Bernoulli theories.
References
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TL;DR: In this article, the integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels.
Journal ArticleDOI
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TL;DR: In this article, a theory of non-local elasticity is presented via the vehicles of global balance laws and the second law of thermodynamics via the use of a localized Clausius-Duhem inequality and a variational statement of Gibbsian global thermodynamics.
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
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
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.