Free vibration of self-powered nanoribbons subjected to thermal-mechanical-electrical fields based on a nonlocal strain gradient theory

This paper is contributed to the studies of dynamic behaviors of a piezoelectric nanoribbon subjected to thermal-mechanical-electrical fields that is used as an approximate model for the self-powered component in medical nanorobots. Both the nonlocal and strain gradient effects are taken into account, and a gradient type of normal strain is introduced and applied instead of the classical normal strain. By combining the theoretical constitutive relations with nonlocal strain gradient piezoelectric equations, the governing equations and boundary conditions under the nonlocal strain gradient theory are derived, respectively, by means of Hamilton's principle and a new definition of nonlocal strain gradient bending moment. The differential quadrature method is used to solve the governing equations numerically and the influences of internal characteristic scales and external physical parameters on dynamic behaviors are discussed. It is demonstrated that the stiffness weakening and strengthening are, respectively caused by the nonlocal and strain gradient effects. The classical results are recovered in case of the same magnitudes for the nonlocal parameter and strain gradient characteristic parameter. There is a coupling between two internal characteristic scales and the peak value of strain gradient characteristic parameter may exist, but effects of internal characteristic parameters and external physical parameters on dynamic behaviors are independent. Additionally, the self-powered nanoribbon may lose its stability with a certain critical external parameter. The work could be useful for the design and realization of self-powered nanostructures.