Transverse free vibration of nanobeams with intermediate support using nonlocal strain gradient theory

In the present study, the transverse free vibration of intermediately supported nanobeams is investigated in the framework of size-dependent nonlocal strain gradient theory. Unlike the classical elasticity theory, nonlocal strain gradient theory considers the micro/nano scale effects in mechanical analysis of size-dependent structures. The potential and kinetic energies have been derived for the nanobeam model and the Ritz method has been used to determine the natural frequencies of intermediately supported nanobeams. A cantilever nanobeam model with intermediate support is considered in the analysis. By changing the position of the intermediate support, dimensionless vibration frequencies of the nanobeam model have been obtained. Obtained results from the present nonlocal strain gradient theory showed that hardening or softening material responses have been observed according to the classical elasticity theory depending on the magnitude of the material length scale parameter and nonlocal scale parameter. This mechanical behavior can provide an advantage to designers while modeling the micro/nanostructures. Present results can be used for the design of nano-sensors, nanotube-based resonators, and oscillators.