000015932 001__ 15932
000015932 005__ 20161115135333.0
000015932 04107 $$aeng
000015932 046__ $$k2013-06-12
000015932 100__ $$aAdhikari, S.
000015932 24500 $$aNonlocal Modal Analysis for Nanoscale Dynamical Systems

000015932 24630 $$n34.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000015932 260__ $$bNational Technical University of Athens, 2013
000015932 506__ $$arestricted
000015932 520__ $$2eng$$aThis paper introduces the idea of nonlocal normal modes arising in the dynamic analysis of nanoscale structures. A nonlocal finite element approach is developed for the axial vibration of nanorods, bending vibration of nanobeams and transverse vibration of nanoplates. Explicit expressions of the element mass and stiffness matrices are derived in closed-form as functions of a length-scale parameter. In general the mass matrix can be expressed as a sum of the classical local mass matrix and a nonlocal part. The nonlocal part of the mass matrix is scale-dependent and vanishes for systems with larger length-scales. New analytical methods are developed to understand the dynamic behaviour of discrete nonlocal systems in the light of classical local systems. The conditions for the existence of classical normal modes for undamped and damped nonlocal systems are established. Closed-form approximate expressions of nonlocal natural frequencies, modes and frequency response functions are derived. Results derived in the paper are illustrated using examples of axial and bending vibration of nanotubes and transverse vibration of graphene sheets.

000015932 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000015932 653__ $$aNormal modes; nonlocal mechanics; finite element; nonlocal frequency.

000015932 7112_ $$aCOMPDYN 2013 - 4th International Thematic Conference$$cIsland of Kos (GR)$$d2013-06-12 / 2013-06-14$$gCOMPDYN2013
000015932 720__ $$aAdhikari, S.$$iGilchrist, D.$$iMurmu, T.$$iMcCarthy, M.
000015932 8560_ $$ffischerc@itam.cas.cz
000015932 8564_ $$s1639331$$uhttps://invenio.itam.cas.cz/record/15932/files/1722.pdf$$yOriginal version of the author's contribution as presented on CD, section: CD-RS 07 DYNAMICS OF MICRO SYSTEMS
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000015932 962__ $$r15525
000015932 980__ $$aPAPER