Nonlinear constitutive piezoelectric cantilever beam with tip mass for energy harvesting, and sensing applications

Abstract Dynamics of a rotating hub and clamped bimorph carrying a tip mass is studied in this paper. In the mathematical model of the structure the classical linear kinematics of the beam deformation is assumed. However, based on experimental results published in literature, the nonlinear formulation of the piezoceramic material constitutive equations is adopted by introducing second-order strain terms. The governing equations of the discussed system are formulated by means of the Hamilton’s principle of least action. The derived system of three coupled nonlinear integro-partial differential equations represents the electro-mechanical behaviour of the beam (transverse displacement and transducer output voltage) and the angular coordinate of the hub. The derived governing equations are reduced by virtue of the Galerkin method and solved numerically around the first resonance zone under periodic torque excitation supplied to the hub. The performed numerical simulations show the system performance for different scenarios of torque excitation, tip mass ratios and electrical boundary conditions.