Nonlinear dynamic response of a multilayer piezoelectric nanocomposite microbeam with tip mass

The nonlinear forced response of multilayer piezoelectric cantilever microbeams reinforced by carbon nanotubes with a concentrated tip mass is investigated. The geometrically exact formulation based on the Cosserat theory of rods is employed to study large amplitude vibrations. The constitutive law of the nanocomposite layers is based on the Eshelby-Mori-Tanaka homogenization approach while the piezoelectric layers are modeled according to the standard piezoelectric constitutive formulation. The enforced inextensibility and unshearability constraints lead to a partial differential equation (PDE) governing the flexural motion of the multilayer microbeams. The obtained PDE is coupled to the ordinary differential equation for the motion of the shuttle mass. The Faedo-Galerkin approach is implemented to discretize the problem. The method of multiple scales is employed to obtain the frequency response of the system under a primary resonance base excitation. The frequency response highlights the effects of the carbon nanotubes volume fraction, tip mass, and force amplitude. An interesting result is obtained showing the feasibility of the second mode exploitation rather than the first mode for mass sensing purposes.