جستجوی مقالات مرتبط با کلیدواژه « سیستم های نانوالکترو مکانیکی » در نشریات گروه « مکانیک »

In this paper, the nonlinear forced vibrations of nonlocal Euler-Bernoulli nanobeam that is utilized in nanoelectromechanical systems are studied using the analytical method of multiple time scales. Based on non-linear strain gradient elasticity theory, governing equation of Euler-Bernoulli nanobeam with von-karman geometric nonlinearity is derived using Hamilton principle. In the next step, using the Galerkin method, the partial differential governing equations for simply supported boundary conditions are reduced to time variable ordinary nonlinear differential equation. Subsequently, the nonlinear forced vibration equation is solved using a multiple time scalar method. After solving the nonlinear excited equation, primary and secondary resonances of nonlocal nanobeam are studied. The region of acceptable sub-harmonic responses is identified and for different values of nonlocal parameter, the frequency response curves and response amplitudes versus excitation amplitude is plotted in all resonances as primary, super-harmonic and sub-harmonic. These results show that using nonlocal strain gradient theory is a fundamental necessity for analyzing nonlinear vibration of nanobeams. The results of this paper can be used to improve the design and optimization of nanoelectromechanical systems.

In this study, nonlinear dynamics of non-classical Kirchhoff plate is analyzed for the first time and the region of chaotic behavior is predicted and controlled by designing the robust adaptive controller. Virtual displacement principle is employed to derive the governing equation of Kirchhoff micro-plate resting on nonlinear elastic foundation. In the governing equation, von Karman geometrical nonlinearity and couple stress theory is considered. Solving the eigen value governing equation for fully simply supported boundary conditions, results are validated. Next, Galerlkin method considering harmonic excitation of first mode is used to derive micro-plate forced vibration equation. Regardless of modal interaction, the chaos threshold is then investigated. Homoclinic orbits of unperturbed system is plotted and stable and unstable manifold transversely cut that is criteria to predict chaos according to Melnikov’s method is studied. Using maximum Lyapunov exponents numerical method, size-dependent chaos is also locally identified. Phase portrait, Poincare mapping and time response are plotted for different values of size ratios and the important effect of size on the chaotic behavior of micro-plats is presented. The results of this study show that chaos in the micro-plats is size dependent and using the non-classical theories to analyze the chaos of micro-plats is necessary. Subsequently, designing the robust adaptive fuzzy controllers, chaotic vibrations are completely eliminated from the system and the robust adaptive fuzzy controller is introduced as an effective method for controlling chaos in these systems. Results of this research can be used in the production process, optimization and control of nanoelectromechanical systems.