With growth of nanotechnology, use of MEMS/NEMS has grown daily. These systems are being used in sensors, resonators, filters and… in a wide range. In Nano-resonators by increasing voltage between two electrodes, applied force increases and will cause movable electrode to stick to fixed electrode. Nonlinearity of applied force, causes nonlinear phenomena and challenged solution of this problem. In dynamic analysis of these systems an important question is that classical governing equations on static and dynamic behavior in which thicknesses are valuable. Experimental results have shown that behavior of micro and Nano-beams in very small thicknesses or classical equations cannot be expressed. For this reason non-classical continuum theory is used for modeling behavior of micro and Nano-beams. In this thesis a silicon beam by considering non-local theory is modeled and governing equations for solving dynamic equations of mode shape and relation of natural frequency with non-local parameters is achieved. Using derived shape mode and Galerkin method differential equations are solved by one of disturbances methods like multiple time scales will be solved. After that frequency response of system near resonance frequency and effect of different parameters on in like actuation amplitude, axial force and effect of size is investigated and compared with classical theory. At last chaotic vibrations investigated and domain of parameters in which chaotic vibrations happen to system will be derived and all of results will be compared with classical theory Keywords: ano-resonator, continuum mechanics theory, non-classical, non-local, multiple time scales, chaotic vibrations
