Nonlinear Restoring Force Identification of Strongly Nonlinear Structures by Displacement Measurement

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.

Soft X-ray emission from an anharmonic collisional nanoplasma by a laser–nanocluster interaction

The purpose of the present paper is to investigate the generation of soft X-ray emission from an anharmonic collisional nanoplasma by a laser–nanocluster interaction. The electric field of the laser beam interacts with the nanocluster and leads to ionization of the cluster atoms, which then produces a nanoplasma. Because of the nonlinear restoring force in an anharmonic nanoplasma, the fluctuations and heating rate of, as well as the power radiated by, the electrons in the nanocluster plasma will be notably different from those arising from a linear restoring force. By comparing the nonlinear restoring force state (which arises from an anharmonic cluster) with that of the linear restoring force (in harmonic clusters), the cluster temperature specifically changes at the resonant frequency relative to the linear restoring force, while the variation of the anharmonic cluster radius is almost identical to that of the harmonic cluster radius. In addition, it is revealed that a sharp peak of X-ray emission arises after some picoseconds in deuterium, helium, neon and argon clusters.

Nonparametric nonlinear restoring force and excitation identification with Legendre polynomial model and data fusion

Identification of nonlinear restoring force and dynamic loadings provides critical information for post-event damage diagnosis of structures. Due to high complexity and individuality of structural nonlinearities, it is difficult to provide an exact parametric mathematical model in advance to describe the nonlinear behavior of a structural member or a substructure under strong dynamic loadings in practice. Moreover, external dynamic loading applied to an engineering structure is usually unknown and only acceleration responses at limited degrees of freedom of the structure are available for identification. In this study, a nonparametric nonlinear restoring force and excitation identification approach combining the Legendre polynomial model and extended Kalman filter with unknown input is proposed using limited acceleration measurements fused with limited displacement measurements. Then, the performance of the proposed approach is first illustrated via numerical simulation with multi-degree-of-freedom frame structures equipped with magnetorheological dampers mimicking nonlinearity under direct dynamic excitation or base excitation using noise-polluted measurements. Finally, a dynamic experimental study on a four-story steel frame model equipped with a magnetorheological damper is carried out and dynamic response measurement is employed to validate the effectiveness of the proposed method by comparing the identified dynamic responses, nonlinear restoring force, and excitation force with the test measurements. The convergence and the effect of initial estimation errors of structural parameters on the final identification results are investigated. The effect of data fusion on improving the identification accuracy is also investigated.