Investigation of Free Vibrations of Stepped Nanobeam Embedded In Elastic Foundation

Abstract

The free vibration of stepped nanobeams embedded in the elastic foundation was investigated using Eringen's nonlocal elasticity theory. It is fixed at the system ends with a simple-simple support. The stepped nanbeam’s equations of motion are obtained by using Hamilton's principle. Multi-time scale, which is the perturbation methods, was used for the analytical solution of the equations. To observe the effects of nano size effect, elastic basis coefficient and step location, natural frequencies of the first three modes of the system were obtained for different non-local parameter values, elastic foundation coefficients, step rates and step positions. In the results, it was seen that the non-local parameter had a negative effect on the natural frequency. The elastic foundation coefficient has been shown to reduce vibration amplitudes.