تحليل كمانش مكانيكي و ارتعاش آزاد نانو صفحه دو لايه ارتوتروپيك با تاثير مقياس اندازه كوچك و تئوري دو متغيره اصلاح شده بوسيله روش سنجش وزني مشتق

چكيده انگليسي :

Mechanical Buckling and Free Vibration Analysis of Double OrthotropicNanoplate Based on Two Variable Refined Plate Theory via Nonlocal Small Scale Effect by DQM Mohammad Hossein Shokrani mh shokrani@me iut ac ir Date of Submission 18 January 2014 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisors Mahdi Salmani Tehrani tehrani@cc iut ac ir Abstract Graphene is a 2D latticed sheet made up of carbon atoms Covalent sp2 bondings between carbon atomsin graphene form an array of hexagons Graphene sheet may be found as a single layer or bilayer types In fact graphene may be regarded as the most popular kind of double orthotropic nanoplate DONP Due to itsamazing mechanical and electrical charactertistics garphene has found a wide range of applications or potentialapplications For example the Young s modulus of graphene is of order 1 TPa the stiffest known material Therefore many studies have been recently carried out to investigate mechanical behavior of DONPs In thisstudy the mechanical buckling and vibration of a double orthotropic rectangular nanoplate which is resting onan elastic foundation is studied The elastic foundation is modeled by the two parameters Pasternak model which is obtained by adding a shear layer to the Winkler model Eringen s nonlocal elasticity theory wasutilized to derive constitutive equations The nonlocal theory accounts for the small scale effects occuring at thenanoscale Also two variable refined plate theory was employed to derive the governing equations of bucklingand vibration In this theory takes the transverse shear effects into account via assuming a parabolic distributionfor the transverse shear strains through the plate thickness Therefore the results obtained from this theory aremore accurate than those obtained from the classical plate theory Then the DQM numerical procedure was usedto solve the governing equations The boundary conditions were imposed using the Shu s direct method Acomputer code wasdeveloped in MATLAB softwareto study the effect of various parameters on the bucklingload and natural frequencies To verify the model and numericalsolution method the numerical results werecompared with those of Navier s solution exact solution and excellent agreement was observed In bucklinganalysis the effect of aspect ratio length to thickness ratio shear loading loading ratio in biaxial loading orthotropic ratio and different boundary conditions on critical buckling load and buckling modes has beenstudied Furthermore the allowable range in which the results of Eringen s nonlocal theory are reliable has beeninvestigated Then the effect of Winkler s stiffness Pasternak s stiffness and Vanderwalls s stiffness on thecritical buckling load has been studied In the analysis of vibrational behavior of the double orthotropicnanoplate the effect of aspect ratio different boundary conditions Winkler stiffness Pasternak stiffness andVander walls stiffness on the natural frequencies and modes has been investigated The results showed thatbuckling load decreases as the nonlocal parameter and loading ratio increase Also it was observed that theeffect of Pasternak stiffness is much more than the other stiffnesses Moreover Vanderwalls stiffness may affectthe buckling load only in out of phase In vibration analysis it was also shown that the natural frequencydecreases as the aspect ratio of the nanoplate increases or the support s stiffness decreases Finally two variablerefined theory and first order shear deformation theory were compared and a very good agreement between theresults of these theories was observed Keywords Double orthotropic nanoplate Mechanical buckling Free vibration Nonlocal theory Two variablerefined plate theory Differential quadrature method

شكراني، محمدحسين

تحليل كمانش مكانيكي و ارتعاش آزاد نانو صفحه دو لايه ارتوتروپيك با تاثير مقياس اندازه كوچك و تئوري دو متغيره اصلاح شده بوسيله روش سنجش وزني مشتق

تئوري غير محلي ارينگن , روش حل عددي سنجش وزني مشتقات