Study of a piecewise linear dynamic system with negative and positive stiffness

Zou, Keguan; Nagarajaiah, Satish

doi:10.1016/j.cnsns.2014.08.016

Cited by 25 publications

(18 citation statements)

References 19 publications

(17 reference statements)

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“…Yang et al [20] studied the dynamic and power flow behavior of a nonlinear vibration isolation system with the negative stiffness mechanism, which can enlarge the frequency band for the effective vibration isolation. Zou and Nagarajaiah [21]. investigated the piecewise linear dynamic oscillator with negative stiffness followed by positive stiffness, which derived approximate the periodic solutions.…”

Section: Introductionmentioning

confidence: 99%

Equivalent bilinear elastic single degree of freedom system of multi-degree of freedom structure with negative stiffness

Huo

et al. 2016

Journal of Sound and Vibration

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a b s t r a c tThe advantage of negative stiffness (NS) is to reduce the structural internal force, especially base shear, which is necessary to be considered during structural design. During design procedures, the structural response should be estimated. For the purpose of estimating the response of the structure with NS, this paper presents an innovative approximate method to transfer a multi degree of freedom (MDOF) structure with NS in the 1st story (MNS1) to an approximate single degree of freedom (SDOF) bilinear elastic system (ASBS). The accuracy of approximation from the MNS1 to the ASBS is studied by the sensitivity method of mode shapes in which the relative changes in structural mode shapes are related to the variation of stiffness. An eight-story numerical example is employed to illustrate the accuracy of approximation by the proposed method. The results show that the accuracy of approach is acceptable, and ASBS can estimate the response of the MNS1.

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Section: Introductionmentioning

confidence: 99%

Equivalent bilinear elastic single degree of freedom system of multi-degree of freedom structure with negative stiffness

Huo

et al. 2016

Journal of Sound and Vibration

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“…Abundant research results have been achieved with respect to analysis and controller design of such PWS system [10][11][12][13][14][15][16]. For instance, the stability and performance of a piecewise linear system were discussed by means of the quadratic and piecewise-quadratic Lyapunov functions which could cast as convex optimization problems and linear matrix inequalities (LMI) by Hassibi and Boyd [10].…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, the stochastic dynamics of the piecewise-smooth structure with negative stiffness under delayed feedback control, which is prone unstable in the dynamic excitations, have not been reported in the literature. Therefore, in this paper, motivated by the work which had been done by Zou and Nagarajaiah [15], a stochastically driven PWS dynamic system with negative stiffness under nonlinear delayed feedback control will be taken into account, which can provide a comprehensive and thorough understanding of the controlled system performance. Initially, negative stiffness in applications other than earthquake has been proposed and used at small scale for the vibration isolation of equipment by Molyneux [24].…”

Section: Introductionmentioning

confidence: 99%

“…According to the work of Zou and Nagarajaiah [15], the restoring force is assumed in the following form:…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, it is also found that the piecewisesmooth approximation is also a powerful tool to approximate the strong nonlinear system, such as the vibration isolation system [13,14]. For example, a nonlinear system with negative stiffness was idealized by using the piecewise linear model in [15], in which numerical and analytical studies were discussed. The passive isolator, which is abstracted from the solid and liquid mixture (SALiM) vibration isolator,…”

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confidence: 99%

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Vibration Analysis of a Piecewise-Smooth System with Negative Stiffness under Delayed Feedback Control

Huang

Yang

et al. 2017

Shock and Vibration

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The principal resonance of a delayed piecewise-smooth (DPWS) system with negative stiffness under narrow-band random excitation is investigated in aspects of multiscale analysis, design methodology of the controller, and response properties. The amplitude-frequency response and steady-state moments together with the corresponding stability conditions of the controlled stochastic system are derived, in which the degradation case is also under consideration. Then, from the perspective of the equivalent damping, the comparisons of the response characteristics of the controlled system to the uncontrolled system, such as the phenomenon of frequency island, are fulfilled. Furthermore, sensitivity of the system response to feedback gain and time delay is studied and interesting dynamic properties are found. Meanwhile, the classification of the steady-state solution is also discussed. To control the maximum amplitude, the feedback parameters are determined by the frequency response together with stability boundaries which must be utilized to exclude the combinations of the unstable parameters. For the case with small noise intensity, mean-square responses present the similar characteristics to what is discussed in the deterministic case.

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Reduction of transmissibility and increase in efficacy of vibration isolation using negative stiffness device with enhanced damping

Nagarajaiah

Zou

Herkal

2022

Structural Contr & Hlth

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Effect of passive vibration isolation heavily depends on force-displacement characteristic of the isolation system. In view of this dependence, this paper investigates the influence of negative stiffness device (NSD) on the effect of vibration isolation system. Detailed evaluation of transmissibility is performed.The critical parameters are identified. It is found that with NSD, significant vibration reduction for both absolute and relative displacement transmissibility is obtained. A modified Lindstedt-Poincaré method (modified L-P method) is used to obtain analytical periodic solutions for the approximated piecewise linear dynamic system. The analytical limit cycles by the modified L-P solution agree satisfactorily with the ones by numerical simulation. The most important finding of this study is that larger damping in a system with NSD helps in reducing transmissibility, thus increasing the efficacy of the isolation system; this is in contrast to other conventional isolation systems, wherein increased structural damping decreases the efficacy of vibration control in the frequency range of interest.

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Study of a piecewise linear dynamic system with negative and positive stiffness

Cited by 25 publications

References 19 publications

Equivalent bilinear elastic single degree of freedom system of multi-degree of freedom structure with negative stiffness

Equivalent bilinear elastic single degree of freedom system of multi-degree of freedom structure with negative stiffness

Vibration Analysis of a Piecewise-Smooth System with Negative Stiffness under Delayed Feedback Control

Reduction of transmissibility and increase in efficacy of vibration isolation using negative stiffness device with enhanced damping

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