Incorporating Dissipated Impact into Random Vibration Analyses through the Modified Hertzian Contact Model

Xu, Ming; Wang, Y.; Jin, Xiaoling; Huang, Zhongdong; Yu, Tongxi

doi:10.1061/(asce)em.1943-7889.0000621

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…e impact f I (X, _ X) is not a constant and depends on the system state when the oscillator collides with the wall. Here, f I (X, _ X) is depicted by the modified Hertzian contact model, shown in Figure 2 [10,16]. It is obvious that the loading process and unloading process are quite different.…”

Section: Vibro-impact Systemmentioning

confidence: 99%

“…e comprehensive impact process is ignored by "classical model", and the restitution coefficient, which is considered as a constant for a random oscillator, is not always reasonable. Recently, one impact model named modified Hertzian contact model, which overcomes the shortages mentioned above, has caught the author's eyes [10]. e impact on the vibrating oscillator is an inelastic force instead of the discontinuous velocity jump.…”

Section: Introductionmentioning

confidence: 99%

“…e impact on the vibrating oscillator is an inelastic force instead of the discontinuous velocity jump. By introducing the modified Hertzian contact model, the stochastic response of the vibro-impact system under Gaussian white noise has been studied by the stochastic averaging [10]. e broadband noises widely existed in the ambient environment and play an important role in dynamic behaviors of mechanical and structural engineering.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Responses for the Vibro‐Impact System under the Broadband Noise

Guan

Ling

2019

Shock and Vibration

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The stochastic averaging is applied to derive the random responses of the SDOF vibro-impact system with one-side wall under additive and multiplicative broadband noise, where the impact is described by the modified Hertzian contact model. Compared with the popular simplified “classical model” (i.e., x˙−=rx˙+), the whole impact process is captured by the modified Hertzian contact model without any assumptions. One example is given to illustrate the proposed technique. The comparison between the analytical results and those from Monte Carlo simulations manifests the accuracy of the proposed technique. It should be pointed out that the technique proposed in this paper is powerful for the cases of weak excitation and big enough bandwidth of the broadband noise. Finally, the influences of various parameters are also discussed in detail.

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Section: Vibro-impact Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic Responses for the Vibro‐Impact System under the Broadband Noise

Guan

Ling

2019

Shock and Vibration

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“…Problems involving the response determination of nonlinear systems under parametric impulsive input are rather common in mechanical and structural engineering. Parametric impulses arise for instance when dealing with problems regarding impacts between objects or objects with a rigid barrier (Dimentberg and Iourtchenko, 2004, Xu et al, 2013 and more generally when dealing with the so-called nonsmooth mechanical systems (Popp, 2000). For example the problem of an elastically restrained and damped bar subjected to a periodic impact load is addressed in Hsu (1997) and Hsu andCheng (1973, 1977), while in Pilipchuky et al (1999) a nonlinear Duffing oscillator under multiplicative impulsive excitation is studied through a non-smooth temporal transformation.…”

Section: Introductionmentioning

confidence: 99%

Direct evaluation of jumps for nonlinear systems under external and multiplicative impulses

Matteo

Paola

Pirrotta

2015

Journal of Vibration and Control

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In this paper the problem of the response evaluation of nonlinear systems under multiplicative impulsive input is treated. Such systems exhibit a jump at each impulse occurrence, whose value cannot be predicted through the classical differential calculus. In this context here the correct jump evaluation of nonlinear systems is obtained in closed form for two general classes of nonlinear multiplicative functions. Analysis has been performed to show the different typical behaviors of the response, which in some cases could diverge or converge to zero instantaneously, depending on the amplitude of the Dirac's delta

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Stochastic averaging for nonlinear vibration energy harvesting system

Jin

Wang

et al. 2014

Nonlinear Dyn

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Incorporating Dissipated Impact into Random Vibration Analyses through the Modified Hertzian Contact Model

Cited by 7 publications

References 17 publications

Stochastic Responses for the Vibro‐Impact System under the Broadband Noise

Stochastic Responses for the Vibro‐Impact System under the Broadband Noise

Direct evaluation of jumps for nonlinear systems under external and multiplicative impulses

Stochastic averaging for nonlinear vibration energy harvesting system

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