Nonlinear vibration control of a membrane antenna structure

In this paper, the active control of nonlinear vibration of a membrane antenna structure is investigated. Considering the geometric nonlinearity of large amplitude vibration of the membrane, the von Karman type geometrical nonlinear strain–displacement relationship is employed in this paper. Then, a nonlinear dynamic model of the membrane antenna structure is established by using the finite element method. It is assumed that the amplitude of vibration of the structure is relatively small when the controller in on, and then a [Formula: see text] robust controller is developed to control the undesired nonlinear vibration of the membrane antenna structure based on the linearized model of the structure. Active control of both the free vibration and forced vibration of the structure are investigated. Numerical simulations are presented to study the nonlinearity of the large amplitude vibration of the structure and the effectiveness of the presented controller.

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Nonlinear Vibration of Temperature-Dependent FG-CNTRC Laminated Beams with Negative Poisson’s Ratio

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455420500431 ◽

2020 ◽

Vol 20 (04) ◽

pp. 2050043 ◽

Cited By ~ 3

Author(s):

Jian Yang ◽

Xu-Hao Huang ◽

Hui-Shen Shen

Keyword(s):

Nonlinear Vibration ◽

Environmental Conditions ◽

Large Amplitude ◽

Vibration Characteristics ◽

Poisson's Ratio ◽

Temperature Dependent ◽

Laminated Beams ◽

Amplitude Vibration ◽

Negative Poisson's Ratio ◽

Large Amplitude Vibration

Laminated beams made of nanocomposite materials have been used in many industrial sectors. This paper reports a study on the vibration behavior of laminated beams when experiencing the large amplitude vibration. The beams are made of perfectly bonded carbon nanotube-reinforced composite (CNTRC) layers. The novel constructions of CNTRC laminated beams with out-of-plane maximum negative Poisson’s ratio (NPR) are proposed. The volume fraction of CNT may change across the beam thickness which results in a piece-wise pattern. The material properties of the CNTRC layers are temperature-dependent and can be estimated by the extended rule of mixture model. The beams are considered to rest on a two-parameter elastic foundation and under differential thermal environmental conditions. The higher order shear deformation beam theory is applied to derive the motion equations of the nonlinear vibration of FG-CNTRC laminated beams. These equations include the influencing factors such as the geometrical nonlinearity in the von Kármán sense, the thermal effects and the beam–foundation interaction. The nonlinear vibration solutions can be obtained by employing a two-step perturbation approach. The nonlinear vibration characteristics of FG-CNTRC laminated beams under different sets of loading conditions and thermal environmental conditions are discussed in detail through a series of parametric studies. Numerical results show that the NPR has a significant effect on the large amplitude vibration characteristics of CNTRC laminated beams.

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Review of the Nonlinear Vibration Analysis of Simply Supported Beams

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.446-449.626 ◽

2012 ◽

Vol 446-449 ◽

pp. 626-629 ◽

Cited By ~ 1

Author(s):

Wen Bin Sun ◽

Wei Zhong He

Keyword(s):

Nonlinear Vibration ◽

Large Amplitude ◽

Vibration Analysis ◽

Complete Understanding ◽

Simply Supported ◽

Amplitude Vibration ◽

Large Amplitude Vibration

The research of large amplitude vibration of simply supported beams can be dated back to 1950; many achievements and some evolution were accomplished by many researchers over hundred and fifty years. The development of nonlinear vibration formulations for beams has gone through distinct phases–earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.

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