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Size-dependent modal interactions of a piezoelectrically laminated microarch resonator with 3:1 internal resonance

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Applied Mathematics and Mechanics(English Edition) 2020年第10期41卷 1517-1538页

作者： A.NIKPOURIAN M.R.GHAZAVI S.AZIZI Mechanical Engineering Department Tarbiat Modares UniversityTehran 14115-111Iran Mechanical Engineering Department Urmia University of TechnologyUrmia 57166-93187Iran

The nonlinear interactions of a microarch resonator with 3:1 internal resonance are studied.The microarch is subjected to a combination of direct current(DC)and alternating current(AC)electric voltages.Thin piezoelectric layers are thoroughly bonded on the top and bottom surfaces of the microarch.The piezoelectric actuation is not only used to modulate the stiffness and resonance frequency of the resonator but also to provide the suitable linear frequency ratio for the activation of the internal resonance.The size effect is incorporated by using the so-called modified strain gradient theory.The system is highly nonlinear due to the co-existence of the initial curvature,the mid-plane stretching resulting from clamped anchors,and the electrostatic excitation.The eigenvalue problem is solved to conduct a frequency analysis and identify the possible regions for activating the internal resonance.The effects of the piezoelectric actuation,the electric excitation,and the small-scale effect are investigated on the internal resonance.Exclusive nonlinear phenomena such as Hopf bifurcation and hysteresis are identified in the microarch response.It is shown that by applying appropriate piezoelectric actuation,one is able to activate microarch internal resonance regardless of the initial rise level of the microarch.It is also disclosed that among all the parameters,AC electric voltage has the greatest effect on the energy exchange between the interacting modes.The results can be used to design resonators and internal resonance based micro-electro-mechanical system(MEMS)energy harvesters.

关键词： microarch resonator internal resonance multiple time scales method micro-electro-mechanical system(MEMS) piezoelectric actuation electrostatic excitation

Broadband energy harvesting based on one-to-one internal resonance

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Chinese Physics B 2020年第10期29卷 195-201页

作者：姜文安马新东韩修静陈立群毕勤胜 Faculty of Civil Engineering and Mechanics Jiangsu UniversityZhenjiang 212013China School of Science Harbin Institute of TechnologyShenzhen 518055China Department of Mechanics Shanghai UniversityShanghai 200072China

We design an electromechanical transducer harvesting system with one-to-one internal resonance that can emerge a broader spectrum vibrations. The novel harvester is composed of a Duffing electrical circuit coupled to a mobile rod, and the coupling between both components is realized via the electromagnetic force. Approximate analytical solutions of the electromechanical system are carried out by introducing the multiple scales analysis, also the nonlinear modulation equation for one-to-one internal resonance is obtained. The character of broadband harvesting performance are analyzed, the two peaks and one jump phenomenon bending to the right for variation of control parameters are observed. It is shown that an advanced bandwidth over a corresponding linear model that does not possess a modal energy interchange.

关键词： energy harvesting internal resonance broadband nonlinear modal interactions

Improving energy harvesting by internal resonance in a spring-pendulum system

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Acta Mechanica Sinica 2020年第3期36卷 618-623页

作者： Wenan Jiang Xiujing Han Liqun Chen Qinsheng Bi Faculty of Civil Engineering and Mechanics Jiangsu UniversityZhenjiang 212013China School of Science Harbin Institute of TechnologyShenzhen 518055China Department of Mechanics Shanghai UniversityShanghai 200072China

This paper proposes a two-to-one internal resonance to widen the bandwidth of vibratory energy harvesters.To describe the improved characteristic,an electromagnetic spring-pendulum harvester is designed.Approximate analytical solutions of the electromechanical coupled system are carried out by introducing the method of multiple scales,and the frequency response relationships of the displacement and the current are obtained.The character of broadband harvesting performance is examined,the two peaks and double jump phenomena for variation of design parameters were observed.The effect of key control parameters on the harvesters bandwidth is considered,and the nonlinear behaviors of the harvester are validated via numerical results.

关键词： Energy harvesting internal resonance Broadband Nonlinear modal interactions

Nonlinear dynamic singularity analysis of two interconnected synchronous generator system with 1:3 internal resonance and parametric principal resonance

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Applied Mathematics and Mechanics(English Edition) 2015年第8期36卷 985-1004页

作者： Xiaodong WANG Yushu CHEN Lei HOU School of Astronautics Harbin Institute of Technology

The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1：3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus （TMIB） power system.

关键词： parametric principal resonance internal resonance singularity method,bifurcation

BIFURCATION IN A PARAMETRICALLY EXCITED TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEM WITH 1∶2 internal resonance

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Applied Mathematics and Mechanics(English Edition) 1999年第4期20卷 11-20页

作者：季进臣陈予恕 Department of Mechanics Tianjin University Tianjin P R China

The nonlinear response of a two_degree_of_freedom nonlinear oscillating system to parametric excitation is examined for the case of 1∶2 internal resonance and, principal parametric resonance with respect to the lower mode. The method of multiple scales is used to derive four first_order autonomous ordinary differential equations for the modulation of the amplitudes and phases. The steady_state solutions of the modulated equations and their stability are investigated. The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions. The Melnikov method is used to study the global bifurcation behavior, the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.

关键词： parametric excitation internal resonance Melnikov method

FORCED VIBRATIONS WITH internal resonance OF A PIPE CONVEYING FLUID UNDER EXTERNAL PERIODIC EXCITATION

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Acta Mechanica Solida Sinica 2011年第6期24卷 477-483页

作者： Feng Liang Bangchun Wen College of Mechanical Engineering Shenyang University of Chemica Technology Shenyang 110142 China School of Mechanical Engineering ＆ Automation Northeastern University Shenyang 110004 China

Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are de- cided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.

关键词： pipe conveying fluid forced vibration internal resonance multidimensional Lindstedt-Poincare method

BIFURCATION ANALYSIS OF A DOUBLE PENDULUM WITH internal resonance

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Applied Mathematics and Mechanics(English Edition) 2000年第3期21卷 255-264页

作者：毕勤胜陈予恕 Department of Mechanics Tianjin University Tianjin P R China

By employing the normal form theory, the Hopf bifurcation and the transition boundary of an autonomous double pendulum with 1:1 internal resonance at the critical point is studied. The results are compared with numeri... 详细信息

关键词： internal resonance Hopf bifurcation transition boundary chaos

In-plane internal resonance analysis of complex cable-stayed bridge under external load

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In-plane internal resonance analysis of complex cable-stayed...

Three-to-one internal resonance of Suspended Cable Accounting for Bending Stiffness

第十届动力学与控制学术会议

作者： HANG Houjun GUO Tieding ZHAO Yueyu College of Civil Engineering Hunan University

Nonlinear dynamics of cable-stayed bridge has been a hot topic due to its complex. A novel nonlinear dynamic model namely, double-cable-stayed shallow-arch, of cable-stayed bridge is established. Especially, the dynamic effect of cable on bridge deck is considered as a transverse excitation, in turn, the deck motion is regarded as a parametric and forced excitation for cables. Based on the governing equations of shallow arch and cables, respectively, the integro differential equations of double-cable-stayed shallow-arch model are derived by considering the join conditions between cables and deck. Then, the in-plane 2:2:1 internal resonance between three first in-plane modes of two cables and shallow arch under both external primary and subharmonic resonance is considered, respectively. The Galerkin discretization technique and the method of multiple scales are applied to obtain the standard modulation equations of the dynamic system. Finally, the numerical simulations are carried out to investigate the dynamic behaviour of the new dynamic system. The results show a rich nonlinear phenomena of cable-stayed bridge and some new phenomena are also observed. For two identical cables located symmetrically at shallow arch, they may have different dynamic behaviours even the initial conditions are identically given. This means that the different branches of equilibrium solutions of system can be observed by two identical cables. For two different cables located symmetrically at shallow arch, the large motion for one of them can be excitated by energy exchange.

关键词： internal resonance modelling cable-stayed bridge bifurcation stability

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Three-to-one Internal Resonance of Suspended Cable Accountin...