تحليل ارتعاشات آزاد نانو صفحات دايره اي و مستطيلي و تاثير نوع شرايط مرزي بر فركانسهاي طبيعي نانو صفحات مستطيلي

چكيده انگليسي :

Free Vibration Analysis of Circular and Rectangular Nanoplates and Effect of Boundary Condition on Natural Frequency of Rectangular Nanoplate Moslem Mohammadi m mohamadi@me iut ac ir Date of Submission 2011 05 23 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Mostafa Ghayour ghayour@cc iut ac irAbstractNanotechnology has the potential of material control and utilization of material properties instruments andmodern systems in nano scale This technology is utilized in different fields like medicine agriculture transportation water and air purification electronics Nano materials have engrossed great deal of attention ofscientific community due to their novel mechanical chemical thermal electrical and electronic properties Graphene sheet is one of the most important productions of nanomaterials As controlled experiments innanoscale are difficult and molecular dynamic simulations are highly computationally expensive theoreticalanalysis of nanostructures becomes an important issue concerning application of nanostructures Grapenesheets are used widely in electronic devices There are three ways for mechanical analysis of these sheets including experiments in nano scale simulation by software and theoretical analysis Continuum modeling ofnanostructures has thus received increasing deal of attention However there is a need to upgrade the classicalcontinuum theories to account for the small scale effects Classical continuum elasticity which is a scale freetheory cannot predict the size effects At nanometer scales size effects often become prominent Bothexperimental and atomistic simulation results have shown a significant size effect in mechanical propertieswhen the dimensions of these structures become small As the length scales are reduced the influences of long range inter atomic and intermolecular cohesive forces on the static and dynamic properties tend to besignificant and cannot be neglected Thus the traditional classical continuum mechanics would fail to capturethe small scale effects when dealing in nano structures The small size analysis using local theory over predictsthe results Thus the consideration of small effects is necessary for correct prediction of micro nano structures Various size dependent continuum theories which capture small scale parameter such as couple stress elasticitytheory strain gradient theory modified couple stress theory are reported These modified continuum theoriesare being used for the analysis of small scale structures However the most reportedly used continuum theoryfor analyzing small scale structures is the Eringen s nonlocal elasticity theory The essence of nonlocalelasticity theory is that the small scale effects are captured by assuming that the stress at a point as a function ofthe strains at all the other points in the domain Nonlocal theory considers long range inter atomic interactionand yields results dependent on the size of a body In this research by using nonlocal elasticity theory oferingen first we investigated vibration analysis of rectangular nanoplates with various boundary conditions bydifferential quadrature method Then we investigated natural frequencies of rectangular nanoplates embeddedin winkler elastic foundation by using differential quadratic method Influence of wrinkle and sheer elasticfactors on natural frequencies are studied By using third order sheer deformation theory and it s assumptionsdisplacement and strain relations are derived Its governing equations are derived by third order sheerdeformation theory Navier s solution is applied to solve governing equation and by using that naturalfrequencies of nanoplate are obtained The refined plate theory is expanded for nanoplates and naturalfrequencies are obtained by refined plate theory for isotropic and orthotropic rectangular nanoplates Thenlateral vibration of rectangular nanoplate under in plane load is investigated Vibration

محمدي، مسلم

تحليل ارتعاشات آزاد نانو صفحات دايره اي و مستطيلي و تاثير نوع شرايط مرزي بر فركانسهاي طبيعي نانو صفحات مستطيلي

تئوري الاستيسيته رينگن , پارامتر اثر مقياس