تحليل ارتعاش و ناپايداري ديناميكي فلاتر و ديورژانس نانو ورق هاي برانگيخته شده با جريان خارجي يك و دو طرفه

چكيده انگليسي :

Vibration Analysis and Dynamic Instability of Flutter and Divergence of Nano Plates Excited by Lateral or Bilateral External Flow Mohammad Reza Matin m matin@me iut ac ir Date of Submission 2012 12 4 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Hamid Reza Mirdamadi hrmirdamadi@cc iut ac ir Mostafa Ghayour ghayour@cc iut ac ir Abstract Laboratory studies show that the mechanical properties and behavior of nano structures are different from other materials The discovery of stable families of carbon nano structures such as graphene sheets GSs fullerenes carbon nano tubes CNTs etc has created a profound impact on nano science and nanotechnology These nano structured materials are basic building blocks of nanotechnology with broad potential applications in the emerging eld of nano electromechanical systems NEMS Theoretical analyses of nanostructures are becoming increasingly important due to dif culties encountered in experiments as the size of physical systems is scaled down into the nanometer scale Of these theoretical analyses atomistic simulations are limited to very small length and time scales due to being computationally expensive Thus the notions of continuum mechanics have attracted a great deal of attention of many researchers to treat structures at the nano scale The vibrational response of nano structures is of great technical importance in nanotechnology theoretically The vibrational response of a nano plate subject to dynamic forces resulting from a fluid flow is considered in this research and the nano plate is transformed into a pressurized channel by adding two rigid walls and a roof Moreover the corresponding critical velocities are obtained resulting from static and dynamic instabilities Narvier Stokes equation is used for modeling the effect of fluid on the plate Furthermore Bernolli s equation for the fluid solid interface and partial differential equation of potential flow are applied to calculate the fluid pressure Classical plate theory is used for formulating nano plate By using nonlocal elasticity theory small size effect is considered for nano plates The fluid flow is considered to be homogeneous laminar fully developed incompressible isothermal uni directional along the length of nano plate and continuous Then by considering the effect of Knudsen Kn and slip boundary condition the effect of nano size is considered for fluid flow Kn affects the dimensionless velocity correction factor VCF parameter directly It is defined as the ratio of average sliding fluid velocity to average no slip fluid velocity Approximate solutions are computed by using Galerkin s weighted residuals method By considering the effects of nonlocal parameter and Kn the critical velocity would reduce Nonlocal parameter could have more effect on reducing the divergence critical velocity of upper modes and coupled mode flutter By comparing the effects of Kn and nonlocal parameter we notice that whenever the fluid is a liquid most of the contribution in decreasing critical flow velocity is due to nonlocal parameter whole and whenever the fluid is a gas Kn has a greater role in decreasing the critical velocity For plate aspect ratios less than 1 i e increasing the width of plate the total plate stiffness would decrease and natural frequencies would become lower than frequencies corresponding to a square plate For plate aspect ratios more than 1 i e decreasing the width of the plate the total plate stiffness would increase and the natural frequencies would become larger than corresponding frequencies of a square plate In summary plate aspect ratio could have impressive effects on the critical flow velocities the temporal order of happening these instabilities and the type of observed instabilities For example increasing aspect ratio could shift the mechanism of instability from a flutter mode toward a divergence one Keywords small size effect fluid str

متين، محمدرضا

تحليل ارتعاش و ناپايداري ديناميكي فلاتر و ديورژانس نانو ورق هاي برانگيخته شده با جريان خارجي يك و دو طرفه

الاستيسته موضعي , اندركنش سيال-سازه , عدد نودسن , شرط مرزي لغزشي , فلاتر