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Determination of the natural frequencies of axially moving beams by the method of multiple scales

Journal of Shanghai University(English Edition) 2007年第3期11卷 251-254页

作者：杨晓东陈立群 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P. R. China Department of Mechanics College of Sciences Shanghai University Shanghai 200444 P. R. China

The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.

关键词： the method of multiple scales natural frequency axially moving beam

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Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions

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Science China(Physics,Mechanics & Astronomy) 2014年第8期57卷 1536-1546页

作者： MA NiuJing WANG RongHui HAN Qiang LU YiGang School of Civil Engineering and Transportation South China University of Technology State Key Laboratory of Subtropical Building Science School of Sciences South China University of Technology

An approach is presented to investigate the nonlinear vibration of stiffened plates.A stiffened plate is divided into one plate and some stiffeners,with the plate considered to be geometrically nonlinear,and the stiffeners taken as Euler *** equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the ***,the effect caused by boundary movement is transformed into equivalent *** first approximation solution of the non-resonance is obtained by means of the method of multiple *** primary parametric resonance and primary resonance of the stiffened plate are studied by using the same *** accuracy of the method is validated by comparing the results with those of finite element analysis via *** examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary *** addition,the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried *** nonlinear vibration characteristics of stiffened plates are obtained,which are useful for engineering design.

关键词： stiffened plates moving boundary nonlinear vibration primary parametric resonance and primary resonance the method of multiple scales

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1:3 Resonant Double Hopf Bifurcation on Two Coupled Limit Cycle Oscillators with Delay Coupling

1:3 Resonant Double Hopf Bifurcation on Two Coupled Limit Cy...

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第十三届全国非线性振动暨第十届全国非线性动力学和运动稳定性学术会议

作者： WANG Wan-yong1,XU Jian1(1.School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

The dynamical behaviour of two coupled limit cycle oscillators around a 1:3 resonant double Hopf bifurcation point is *** parameters including time delay are chosen as the bifurcation parameters,then the method of multiple scales is used to obtain bifurcation *** analyzing the bifurcation equations,the dynamical behaviour arising from the bifurcation is classified qualitatively in two-parameter cross-section by fixing one of the three bifurcation *** results show rich dynamical phenomena including the amplitude death,periodic solution and quasiperiodic *** particular,by varying time delay,the exchange of energy between two oscillators is *** simulation results are also given to support the theoretical predictions.

关键词： the method of multiple scales resonance double Hopf bifurcation time delay

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Nonlinear modal analysis of a kind of variable cross-section composite beam

Nonlinear modal analysis of a kind of variable cross-section...

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第十届动力学与控制学术会议

作者： Xuan Ling Zhang YingHui Li School of Mechanics and Engineering Southwest Jiaotong University

In this paper, the reduced stiffness matrix for laminated beam is obtained when the poisson effect is *** to the Hamilton’s principle, two nonlinear governing equations in transverse and axial directions are derived based on Euler-Bernoulli beam theory and vonKármán geometric nonlinearity. Neglecting the axial intertia and damping, the two nonlinear equations reduced to a singal equation for investigating transverse nonlinear vibration.A kind of variable cross-section composite beam is considered. The linear frequencies is verified by an open literature. Aiming at symmetric and asymmetric layup orientations, the nonlinear nature frequencies are obtained and the corresponding nonlinear normal modals are constructed by the method of multiple scales.

关键词： Poisson effect Nonlinear Euler-Bernoulli beam theory Variable crosssection laminated beam Nonlinear normal modal the method of multiple scales

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Research on Electromechanical Coupling and Bending-Torsion Vibration of the Belt Driver Mechanism

Research on Electromechanical Coupling and Bending-Torsion V...

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第二十九届中国控制会议

作者： LI Gaofeng,YANG Zhi-An1,XIN Jing21.Key Laboratory of Structure and Vibration Engineering of Tangshan and Tangshan College,Tangshan 063000,P.R.China 2.College of Mechanical Engineering,Hebei Polytechnic University,Tangshan 063009,P.R.China

The belt driver mechanism of the electromechanical coupling and bending-torsion coupled nonlinear vibration differential equations are established according to Lagrange-Maxwell equation and the numerical analysis are carried *** of the nonlinear characteristics of electromechanical coupling system are analyzed by means of Runge-Kutta *** phase diagram,time response,frequency map and axis trajectory are *** is obvious unstable phenomena when motor in state of rated *** effect of torsional vibration on motor is not obvious.

关键词： Belt Nonlinear Vibration the method of multiple scales Electromechanical Coupling

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Study on Primary Resonance of Ceramic and Metal Functionally Graded Material Rectangular Plate Subjected to Mechanical Force

Study on Primary Resonance of Ceramic and Metal Functionally...

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第二十九届中国控制会议

作者： YANG Zhi-An1,JIA Shang-Shuai21.Tangshan College and Tangshan Key Laboratory of Structure and Vibration Engineering,Tangshan 063000,P.R.China 2.College of Mechanical Engineering,Hebei Polytechnic University,Tangshan 06300,P.R.China

According to the nonlinear dynamics equation of the functionally graded material rectangular plate,the nonlinear vibration equation of ceramic and metal functionally graded material rectangular plate subjected to mechanical force excitation is obtained in order to study primary resonance of ceramic and metal functionally graded material rectangular plate subjected to mechanical force *** means of the method of multiple scales,the approximation solution of primary resonance of the system is acquired,and numerical analysis of the influence of damping excitation as well as geometric parameters on amplitude frequency response curve of the primary resonance system is carried out.

关键词： Functionally Graded Material Nonlinear Vibration the method of multiple scales Primary Resonance Amplitude Frequency Response Curves

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