|
Inherent nonlinearities of piezoelectric materials are inevitably pronounced in various engineering applications
such as sensing, actuation, their combined applications for vibration control, and most recently, energy harvesting
from dynamical systems. The existing literature focusing on the dynamics of electroelastic structures
made of piezoelectric materials have explored such nonlinearities in a disconnected way for the separate problems
of mechanical and electrical excitation such that nonlinear resonance trends have been assumed to be due to
different additional terms in constitutive equations by different researchers. Similar manifestations of softening
nonlinearities have been attributed to purely elastic nonlinear terms, coupling nonlinearities, hysteresis, or a
combination of these effects, by various authors. However, a reliable nonlinear constitutive equation for a given
piezoelectric material is expected to be rather unique and valid regardless of the application, e.g. energy harvesting,
sensing, or actuation. A systematic approach focusing on the two-way coupling can result in a sound
mathematical framework. To this end, the present work investigates the nonlinear dynamic behavior of a bimorph
piezoelectric cantilever under low-to-high mechanical and electrical excitation levels in energy harvesting,
sensing, and actuation. A physical model is proposed including both ferroelastic hysteresis, stiffness, and electromechanical
coupling nonlinearities. A lumped parameter electroelastic model is developed by accounting for
these nonlinearities to analyze the primary resonance of a cantilever using the method of harmonic balance.
Strong agreement between the model and experimental investigation is found, providing solid evidence that the
the dominant source of observed softening nonlinear effects in geometrically linear piezolectric cantilever beams
is well represented by a quadratic term resulting from ferroelastic hysteresis. Electromechanical coupling and
cubic softening nonlinearities are observed to become effective only near the physical limits of the brittle and stiff
bimorph cantilever used in the experiments, revealing that the quadratic nonlinearity associated with hysteresis
has the primary role in nonlinear nonconservative dynamic behavior.
|
