Nonlinear Restoring Force Identification of Strongly Nonlinear Structures by Displacement Measurement

2021 ◽  
pp. 1-29
Author(s):  
Qinghua Liu ◽  
Zehao Hou ◽  
Ying Zhang ◽  
Xingjian Jing ◽  
Gaëtan Kerschen ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Vibration Isolation ◽  
Displacement Measurement ◽  
Identification Accuracy ◽  
Geometrical Parameters ◽  
Nonlinear Structures ◽  
Restoring Force ◽  
Experimental Conditions ◽  
Strongly Nonlinear ◽  
Nonlinear Restoring Force

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.

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

2021 ◽  
pp. 147592172199474
Author(s):  
Bin Xu ◽  
Ye Zhao ◽  
Baichuan Deng ◽  
Yibang Du ◽  
Chen Wang ◽  
...  
Keyword(s):  
Data Fusion ◽  
Legendre Polynomial ◽  
Structural Parameters ◽  
Polynomial Model ◽  
Magnetorheological Damper ◽  
Dynamic Responses ◽  
Identification Accuracy ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Dynamic Loadings

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.

scholarly journals An Analytical Approximation Method for Strongly Nonlinear Oscillators

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Wang Shimin ◽  
Yang Lechang
Keyword(s):  
Vibration Amplitude ◽  
Analytical Approximation ◽  
Frequency Characteristics ◽  
Restoring Force ◽  
Strongly Nonlinear ◽  
Nonlinear Restoring Force ◽  
Forced Oscillators ◽  
Stationary Vibration ◽  
Derivatives Of ◽  
Strongly Nonlinear Oscillators

An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.

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

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
R. Nemati Siahmazgi ◽  
S. Jafari
Keyword(s):  
Electric Field ◽  
Laser Beam ◽  
Resonant Frequency ◽  
Restoring Force ◽  
Cluster Radius ◽  
X Ray ◽  
Nonlinear Restoring Force ◽  
Cluster Temperature ◽  
Argon Clusters ◽  
Helium Neon

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.

An experimental study of strongly nonlinear waves in a rotating system

1987 ◽  
Vol 177 ◽  
pp. 381-394 ◽  
Author(s):  
Dominique P. Renouard ◽  
Gabriel Chabert D'Hières ◽  
Xuizhang Zhang
Keyword(s):  
Equilibrium Shape ◽  
Scaling Law ◽  
Maximum Amplitude ◽  
Rotating Platform ◽  
Coriolis Parameter ◽  
Rotating System ◽  
Height Variation ◽  
Experimental Conditions ◽  
Strongly Nonlinear ◽  
The Right

The influence of rotation upon internal solitary waves is studied in a (10 m × 2 m × 0.6 m) channel located on the large rotating platform at Grenoble University. We observe an intumescence which moves along the right-hand side of the channel with respect to its direction of propagation. Along the side, once the intumescence reaches its equilibrium shape, the height variation of the interface with time is correctly described by the sech2 function, and the characteristic KdV scaling law linking the maximum amplitude and the wavelength along the side is fulfilled. The intumescence is a stable phenomenon which moves as a whole without deformation apart from the viscous damping. For identical experimental conditions, the amplitude of the intumescence along the side increases with increasing Coriolis parameter, and at a given period of rotation of the platform, the celerity along the side increases with increasing amplitude. But for identical conditions, we found that the celerity along the side is equal to the celerity that the wave would have for such conditions without rotation. The amplitude of the intumescence in a plane perpendicular to the wall decreases exponentially with increasing distance from the side, but the crest of the wave is curved backward.

Design of mechanical metamaterials for simultaneous vibration isolation and energy harvesting

2017 ◽  
Vol 111 (25) ◽  
pp. 251903 ◽  
Author(s):  
Ying Li ◽  
Evan Baker ◽  
Timothy Reissman ◽  
Cheng Sun ◽  
Wing Kam Liu
Keyword(s):  
Energy Harvesting ◽  
Vibration Isolation ◽  
Mechanical Metamaterials

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

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