By Adhikari, Sondipon; Karličić, Danilo; McCarthy, Michael; Murmu, Tony
Serving as a evaluate on non-local mechanics, this e-book offers an creation to non-local elasticity thought for static, dynamic and balance research in quite a lot of nanostructures. The authors draw on their lonesome learn adventure to provide primary and complicated theories which are suitable throughout quite a lot of nanomechanical platforms, from the basics of non-local mechanics to the newest learn applications.
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Additional resources for Non-local structural mechanics
11. Concept of non-local elasticity It is well known that one of the basic principles of classical continuum mechanics is that it eliminates the influence of strains field of distant points on the reference point. Non-local continuum theory, or non-local elasticity theory, on the other hand, incorporates these distant effects known as nonlocal effects. The essence of the non-local elasticity theory is that the stress field at a reference point in an elastic continuum depends not only on strain at that point but also on the strain at every other point ′ in the domain [AMA 10, BES 11, ECE 07, ERI 83, HEI 10, RED 08].
KAR 15] performed a detailed analysis of the free longitudinal vibrational response of the system with coupled viscoelastic nanorods and investigated the influence of different physical parameters on complex natural frequencies. Murmu and Adhikari [MUR 10] analyzed the longitudinal vibration of double-nanorod system (DNRS) coupled with an elastic layer. They investigated the effects of the non-local parameter, layer stiffness and aspect ratio on the free longitudinal vibration of DNRS. Moreover, Karličić et al.
On the contrary, only a limited amount of work is devoted to the longitudinal vibration of nanobeams and nanoplates. In what follows, we will review some of the papers where the free or forced vibration of complex systems based on nanorods coupled with elastic, viscoelastic or other types of layers are examined for various boundary conditions, aspect ratios and small-scale parameter. Danesh et al. [DAN 12] accounted for the small-scale effect in the longitudinal vibration of tapered nanorod using the non-local elasticity theory.