Investigation of vibration behavior of supported nano beams according to nonlocal elasticity theory

Nanostructures like nanobeam, plate, rod, shell, etc. find wide application field in nanodevices such as nanoelectromechanical systems, nanosensors. The study of the vibrational behavior of the nano structures great interest to researchers. The vibrational behavior of nano structures are studied with different approaches and various perspectives. Most of the studies have been conducted in the light of size-dependent theories. Non-classical continuity theories like Eringen's nonlocal elasticity theory, modified coupled stress theory, stress gradient theory, etc. have been used by many authors to study the vibrational behavior of nanostructures. Eringen's non-local theory is based on the assumption that stress at a point is a function of stresses at all points in the continuum. Therefore, it has proven to be the most accepted theory in the literature about the size-dependent of nanostructures. For this reason, the non-local elasticity theory of Eringen was used in the presented thesis. Equations of motion are obtained using Hamilton's principle based on non-local theory. After the equations of motion were written in dimensionless form, they have solved analytically by applying the method of multiple scales. Amplitude phase modulation equations are derived for different states of forcing frequency. Support numbers and support positions of multi-support nanobeams constitute the main purpose of the study. It has been shown that the number of supports and the positions of the supports are of great importance in the vibration movements of nanobeams. In addition, the non-local parameter effect and the states of the different modes are examined. Linear natural frequencies of different scenarios of support numbers and positions have been found. The nonlinear behaviors of the scenarios of interest were examined by drawing frequency response curves. The variation of nonlinear frequency of different states of variable parameters was analyzed. Increasing the non-local parameter value in the analysis have a significant effect on the nonlinear natural frequency and frequency response curves. As the increase of the mode, the clarity of the results increases as in the non-local parameter values.