The dynamic stability in transverse vibration of a viscoelastic pipe for conveying puisative fluid is investigated for the simply-supported case. The material property of the beammodel pipe is described by the Kelvin-...The dynamic stability in transverse vibration of a viscoelastic pipe for conveying puisative fluid is investigated for the simply-supported case. The material property of the beammodel pipe is described by the Kelvin-type viscoelastic constitutive relation. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. The method of multiple scales is applied directly to the governing partial differential equation without discretization when the viscoelastic damping and the periodical excitation are considered small. The stability conditions are presented in the case of subharmonic and combination resonance. Numerical results show the effect of viscosity and mass ratio on instability regions.展开更多
The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating ci...The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.展开更多
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-am...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.展开更多
研究轴向运动梁在外激励力作用下非线性振动的联合共振问题。利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用G a lerk in方法离散运动方程。采用IHB法进行非线性振动求解,分析在内...研究轴向运动梁在外激励力作用下非线性振动的联合共振问题。利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用G a lerk in方法离散运动方程。采用IHB法进行非线性振动求解,分析在内共振条件且外激励作用下的联合共振问题,对周期解进行稳定性的判定。典型算例获得了不同外激励力振幅时系统非线性振动的复杂频幅响应曲线。展开更多
Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of aut...Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonsWated. It is found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10372063).
文摘The dynamic stability in transverse vibration of a viscoelastic pipe for conveying puisative fluid is investigated for the simply-supported case. The material property of the beammodel pipe is described by the Kelvin-type viscoelastic constitutive relation. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. The method of multiple scales is applied directly to the governing partial differential equation without discretization when the viscoelastic damping and the periodical excitation are considered small. The stability conditions are presented in the case of subharmonic and combination resonance. Numerical results show the effect of viscosity and mass ratio on instability regions.
基金Supported by National Natural Science Foundation of China(Grant No11472239)Hebei Provincial Natural Science Foundation of China(Grant No.A2015203023)Key Project of Science and Technology Research of Higher Education of Hebei Province of China(Grant No.ZD20131055)
文摘The rotating circular plate is widely used in mechanical engineering, meanwhile the plates are often in the electromagnetic field in modern industry with complex loads. In order to study the resonance of a rotating circular plate under static loads in magnetic field, the nonlinear vibration equation about the spinning circular plate is derived according to Hamilton principle. The algebraic expression of the initial deflection and the magneto elastic forced disturbance differential equation are obtained through the application of Galerkin integral method. By mean of modified Multiple scale method, the strongly nonlinear amplitude-frequency response equation in steady state is established. The amplitude frequency characteristic curve and the relationship curve of amplitude changing with the static loads and the excitation force of the plate are obtained according to the numerical calculation. The influence of magnetic induction intensity, the speed of rotation and the static loads on the amplitude and the nonlinear characteristics of the spinning plate are analyzed. The proposed research provides the theory reference for the research of nonlinear resonance of rotating plates in engineering.
基金the National Natural Science Foundation of China (Nos. 10702045 and 10872135)the Aerospace Foundation of China (No. 2009ZA018)the Natural Science Foundation of Liaoning Province (No. 2009A572)
文摘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.
文摘研究轴向运动梁在外激励力作用下非线性振动的联合共振问题。利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用G a lerk in方法离散运动方程。采用IHB法进行非线性振动求解,分析在内共振条件且外激励作用下的联合共振问题,对周期解进行稳定性的判定。典型算例获得了不同外激励力振幅时系统非线性振动的复杂频幅响应曲线。
文摘Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonsWated. It is found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.
