Free Vibrations Analysis of Stepped Nanobeams Using Nonlocal Elasticity Theory

. Free vibration of stepped nanobeams was investigated using Eringen's nonlocal elasticity theory. Beam analysis is based on Bernoulli-Euler theory and nanoscale analysis is based on Eringen's nonlocal elasticity theory. The system boundary conditions were determined as simple-simple. The equations of motion of the system were obtained using Hamilton's principle. For the solution of the obtained state equations, a multi-time scale, which is one of the perturbation methods, was used. The results part of the study, it is aimed to observe the nano-size effect and the effects of the step state. For this purpose, the natural frequency values of the first three modes of the system were obtained for different non-local parameter values, step rates, and step positions. When the results were examined, it was determined that the non-local parameter value, step ratio, and natural frequency were inversely proportional to each other. In addition, to strengthen the accuracy of the results, the results obtained were compared with the results of other studies in the literature conducted under the specified conditions, and a perfect agreement was observed. The current beam model, on the other hand, could help design and manufacture ICs such as nano-sensors and nano-actuators.