Identification of Stiffness Force in Nonlinear Piezoelectric Structures Based on Hilbert Transform

Nonlinear piezoelectric structures have attracted great attention in energy harvesting, vibration control, and morphing structures recently. The most important design and dynamic analysis parameters in a nonlinear piezoelectric structure is the nonlinear stiffness force. However, the nonlinear stiffness force is difficult to calculate analytically or measure statically under complicated practical engineering conditions. Therefore, this paper utilizes signal decomposition and the Hilbert transform-based method for the precise identification of stiffness force of a class of typical nonlinear piezoelectric structures. The quasi-zero stiffness, bistable stiffness, and tristable stiffness structures are designed in the magnetic coupled piezoelectric cantilever beam system. The identification process and the applicability based on free vibration and forced frequency-swept response for different nonlinear structures will be discussed. Numerical examples of quasi-zero stiffness, bistable stiffness, and tristable stiffness nonlinear piezoelectric structures show the necessity to choose the reasonable free decay and the forced frequency-swept response for accurate identification. In the experimental condition, the identified nonlinear stiffness force keeps in good agreement with the measurement by the dynamometer.