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ParametricVibration Analysis of Pipes Conveying Fluid by nonlinear normal modes and a Numerical Iterative Approach

Advances in Applied Mathematics and Mechanics 2019年第1期11卷 38-52页

作者： Feng Liang Xiaodong Yang Wei Zhang Yingjing Qian Roderick V.N.Melnik College of Mechanical Engineering Yangzhou UniversityYangzhou 225127JiangsuChina Beijing Key Laboratory of nonlinear Vibrations and Strength of Mechanical Engineering College of Mechanical Engineering and Applied ElectronicsBeijing University of TechnologyBeijing 100124China The MS2Discovery Interdisciplinary Research Institute M2NeT LaboratoryWilfrid Laurier University75 University Avenue WestWaterlooONCanadaN2L 3C5 BCAM–Basque Center for Applied Mathematics E48009 BilbaoSpain

nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic *** nonlinear non-autonomous governing equations are transformed into a set of pseudo-autonomous ones by employing the harmonic balance *** nonlinear normal modes are constructed by the invariant manifold method on the state space and a numerical iterative approach is adopted to obtain numerical solutions,in which two types of initial conditions for the modal coefficients are *** results show that both initial conditions can lead to fast *** frequency-amplitude responses with some modal motions in phase space are obtained by the present iterative *** phase difference and traveling waves are found in the time-domain complex modal analysis.

关键词： Gyroscopic continua pipes conveying pulsating fluid parametric vibration nonlinear normal modes iterative approach

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nonlinear modal electromechanical coupling factor for piezoelectric structures containing nonlinearities

引用

Chinese Journal of Aeronautics 2023年第2期36卷 100-110页

作者： Yaguang WU Yu FAN Lin LI School of Energy and Power Engineering Beihang UniversityBeijing 100191China Beijing Key Laboratory of Aero-engine Structure and Strength Beijing 100191China

Within the linear framework,the Modal Electromechanical Coupling Factor(MEMCF)is an important indicator to quantify the dynamic conversion of mechanical energy and electrical energy of piezoelectric *** is also an important tool to guide the piezoelectric damping design of linear *** aircraft often fly in maneuvers,and the variable working conditions induce drastic changes in the load level on *** and contact nonlinearities of thin-walled structures and joint structures are often *** achieve a good vibration reduction effect covering all working conditions,one cannot directly use linear electromechanical coupling theory to instruct the piezoelectric damping design for nonlinear ***,this paper defines the nonlinear Modal Electromechanical Coupling Factor(NMEMCF)and proposes the corresponding numerical method for the first time to quantitatively evaluate the electromechanical coupling capability of nonlinear piezoelectric *** candidate definitions of the NMEMCF are given,including two frequency definitions and one energy *** energy definition is the most promising *** is not only applicable to both conservative and dissipative nonlinear structures but also compatible with the linear *** addition,based on the energy formula,the NMEMCF can be obtained by only performing one nonlinear modal analysis in the open-circuit *** analytical findings and the numerical tool are validated against two piezoelectric structures with different types of nonlinearities.A strong correlation among the NMEMCF,geometric parameters,and energy dissipation is *** results confirm that the proposed NMEMCF captures the physics of the electromechanical coupling phenomenon associated with nonlinear piezoelectric structures and can be used as an essential design indicator of piezoelectric damping,especially for variable working conditions.

关键词： Modal electromechanical coupling factor Multiharmonic balance method nonlinear normal modes Piezoelectric damping Vibration control

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