Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment

In this article, transverse vibration of rotary functionally graded size-dependent tapered Bernoulli–Euler nanobeam in thermal environment at low temperature has been investigated based on Eringen's nonlocal theory for cantilever and propped cantilever boundary conditions. Material properties of FG nanobeam are supposed to be temperature dependant and vary continuously along the thickness according to the power-law form. The axial force is also included in the model as the true spatial variation due to the rotation. The nonlocal equations of motion are derived through Hamilton's principle and they are solved by the differential quadrature method. Validations are done by comparing available literatures and obtained results, which reveal the accuracy of the applied method. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters, such as angular velocity, material distribution profile, different boundary conditions, small-scale parameter and rate of cross-section change on the first three nondimensional natural frequencies of the rotary FG nanobeam in detail. Numerical results are presented to serve as benchmarks for the application and the design of nanoelectronic, nanodrive devices and nanomotor, in which nanobeams act as basic elements. They can also be useful as valuable sources for validating other approaches and approximate methods.The results of this article are suitable in designation of micromachines, such as micromotors and micro-rotors.