Parameter identification of nonlinear bistable piezoelectric structures by two-stage subspace method

Liu, Qinghua; Cao, Junyi; Hu, Fangyuan; Li, Dan; Jing, Xingjian; Hou, Zehao

doi:10.1007/s11071-021-06738-z

Cited by 16 publications

(3 citation statements)

References 40 publications

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“…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]. Liu et al developed a two-stage nonlinear subspace identification method to identify the nonlinear restoring force in a bistable piezoelectric energy harvesting structure [25]. Zhu et al introduced the Bayesian model selection in nonlinear subspace identification and utilized this method in a bistable stiffness system [26].…”

Section: Introductionmentioning

confidence: 99%

Physics-informed sparse identification of bistable structures

Liu¹,

Zhao²,

Zhang³

et al. 2022

J. Phys. D: Appl. Phys.

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The design of bistable structures is a hot topic in the last decade due to its wide application in smart actuators, energy harvesters, flexible robotics, etc. The characterization of the nonlinear restoring force of bistable structures plays a significant role in modeling and enhancing dynamic performance. However, the traditional nonparametric identification methods may have insufficient accuracy or even be invalid because of numerical differentiation procedures and static fitting. Besides, the modern data-driven sparse regression identification methods rely highly on the assumed nonlinear basis functions and lack interpretability. In this paper, a physics-informed sparse identification method is proposed for the nonlinear restoring force identification of bistable structures. The function of the nonlinear restoring force is physically informed by the derived equation of the Hilbert transform and parameter fitting. Furthermore, sparse identification is conducted based on the free vibration responses of the bistable vibrator. The numerical studies verify the effectiveness of the proposed algorithm under the noise level of 30dB. Experimental measurement is conducted on a magnetic coupled bistable beam to perform the model identification. It has been demonstrated that the reconstructed dynamic response and nonlinear restoring force both keep in good agreement with the measured ones.

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Section: Introductionmentioning

confidence: 99%

Physics-informed sparse identification of bistable structures

Liu¹,

Zhao²,

Zhang³

et al. 2022

J. Phys. D: Appl. Phys.

Self Cite

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“…This class of methods include the nonlinear subspace identification (NSI) technique [21,22] and the polynomial nonlinear state-space approach (PNLSS) [23]. The former in particular is based on the feedback interpretation of the nonlinearity [24,25] combined with the classical subspace identification framework, and it has been adopted to identify both localized and distributed nonlinearities [26][27][28], and bistable systems [29][30][31]. In order to adopt the NSI technique, the following prior information must be known/assumed: (1) the functional form of the nonlinearities of the system, in the following called ''nonlinear basis functions''; (2) the location of the nonlinearities (in the case of localized nonlinear behavior).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework

Anastasio

Marchesiello

2023

Nonlinear Dyn

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In this paper, the periodic solutions of nonlinear mechanical systems are studied starting from the nonlinear state-space model estimated using the nonlinear subspace identification (NSI) technique. In its standard form, NSI needs the input–output data from a nonlinear structure undergoing broadband excitation and requires the prior knowledge of the locations and kind of nonlinearities to be estimated. The method allows the estimation of the nonlinear features of the system and the indirect study of its periodic solutions using a single broadband excitation, without the need of feedback control loops. To this end, the nonlinear frequency response curves of the system are estimated merging the harmonic balance method with the NSI technique and using a continuation approach. Then, a monodromy-based stability analysis is developed in the nonlinear state-space framework to study the stability of the periodic solutions of the system and to track its bifurcations. The method is validated considering conservative nonlinearities on two numerical examples and one experimental application, the latter comprising a double-well oscillator with period-doubling phenomena. The effects of noise and nonlinear modeling errors are also evaluated.

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“…Bistable structures are structures that not only have negative stifness properties, but can also provide cubic stifness to enhance vibration control. Most previous studies focused on mechanical properties analysis [38,39] and vibration isolation applications of bistable structures. Johnson et al [40] studied the vibration-attenuating efect of a bistable oscillator and investigated its snap-through dynamics using the harmonic balance method and experimentation.…”

Section: Introductionmentioning

confidence: 99%

Development of a Negative Stiffness Bistable Damper for Structural Vibration Control

Fan

Huang

Huo

2022

Shock and Vibration

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Linear dampers have been widely applied for suppressing the dynamic responses of structures to mitigate their damage. However, the primary disadvantage of the classical linear damper is that it is vulnerable to detuning, which has become an issue of great importance recently due to a great reduction in vibration control performance. To overcome the shortcoming, this study develops a negative stiffness bistable damper (NSBD) composed of a simple assembly consisting of a bistable buckling beam with a mass. Energy is dissipated through the transformation between the bistable states. The constitutive equation of the NSBD is derived to analyze the effects of the stiffness ratio, the arch-span ratio, and the damping ratio on its restoring capabilities. The vibration reduction effect of the NSBD is experimentally evaluated under different sinusoidal and seismic excitations in shaking table tests. The obtained results reveal that the NSBD can effectively restrain structural displacements.

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Parameter identification of nonlinear bistable piezoelectric structures by two-stage subspace method

Cited by 16 publications

References 40 publications

Physics-informed sparse identification of bistable structures

Physics-informed sparse identification of bistable structures

Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework

Development of a Negative Stiffness Bistable Damper for Structural Vibration Control

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