Nonlinear Restoring Force Identification of Strongly Nonlinear Structures by Displacement Measurement

Abstract

Strongly nonlinear structures have attracted a great deal of attention in energy harvesting and vibration isolation recently. However, it is challenging to accurately characterize the nonlinear restoring force using analytical modeling or cyclic loading tests in many realistic conditions due to the uncertainty of installation parameters or other constraints, including space size and dynamic disturbance. Therefore, a displacement-measurement restoring force surface identification approach is presented for obtaining the nonlinear restoring force. Widely known quasi-zero stiffness, bistable and tristable structures are designed in a cantilever-beam system with coupled rotatable magnets to illustrate the strongly nonlinear properties in the application of energy harvesting and vibration isolation. Based on the derived physical model of the designed strongly nonlinear structures, the displacement-measurement restoring force surface identification with a least-squares parameter fitting is proposed to obtain the parameters of the nonlinear restoring force. The comparison between the acceleration integration and displacement differentiation methods for describing the restoring force surface of strongly nonlinear structures is discussed. Besides, the influence of the noise level on identification accuracy is investigated. In experimental conditions, quasi-zero stiffness, bistable, and tristable nonlinear structures with various geometrical parameters are utilized to analyze the identified nonlinear restoring force curve and measured force-displacement trajectory. Finally, experimental results verify the effectiveness of the displacement-measurement restoring force surface method to obtain the nonlinear restoring force.

Physics-informed sparse identification of bistable structures

“…In addition to nonlinear monostable structures, some improved signal processing methods have been extended to the nonlinear restoring force identification of bistable structures. Liu et al comparatively investigated the displacement and acceleration measurement restoring force surface method for identifying nonlinear restoring force and damping coefficient in bistable cantilever beams [22]. Anastasio combined restoring force surface and nonlinear subspace methods to estimate an asymmetric double-well Duffing system's nonlinear stiffness and damping characters [23,24].…”