Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor...Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor system in aero-engines. The motion equations are derived through Lagrange method. The relationship between structural and mechanics characteristics parameters are built up. Finally, the dynamic influence of bearing misalignment on rotor system are divided into three kinds： additional rotor bending rigidity, additional bearing misalignment excitation force and additional imbalance. The equations suggest that additional imbalance excitation force activates the nonlinearity on rotor system and an additional 2x excitation force might appear.展开更多
Urban trains running on ground surface lead to evironmental ground vibrations in the vicinity of railwaylines. The complicated vibration source of the system can hardly be measured directly. The inversion methodology ...Urban trains running on ground surface lead to evironmental ground vibrations in the vicinity of railwaylines. The complicated vibration source of the system can hardly be measured directly. The inversion methodology in engineering seismology is borrowed here to study the dynamic exciting sourec, i.e., the wheel-rail unevenness. A dynamic coupled train-track-3D ground model is combined with a genetic algorithm for the inversion. The solution space of the inversion variables, the objective function and the solving genetic strategy of the inversion are determined, and a joint inversion for the wheel-rail unevenness source function and some track structure parameters is therefore designed. The wheel-rail unevenness PSD, being the source function of No. 13 Beijing urban railway, is obtained by the inversoin based on observed data in the field. The result indicates that the source function discribes the track unevenness in the range of wavelength over 1.2 m, and reflects properly wheel irregularites in the range of wavelength shorter than 1.2 m. It should be noticed that the urban rail traffic is not very fast, and this range of short wavelength is exactly corresponding to the main frequency band of environmental vibrations from the traffic. The unevenness of wavelength under 1.2 m is underestimated, and the ground vibration in the main frequency band must be underestimated consequently, if the track unevenness spectrum is taken as the source function. Rather than the track spectrum reflecting just the evenness of track, the wheel-rail spectrum expresses both the track unevenness and the irregularities of wheels, and therefore is more suitable to be the source function of urban railway traffic. It is also convinced that the exciting source inversion according to observed ground vibrations is an effective way to detect quantitatively the combined wheel-rail unevenness.展开更多
In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied.The damping,parametric...In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied.The damping,parametrical excitation and the nonlinearities are regarded as weak.The averaged equation depicting the fast and slow dynamics is derived through the method of multiple scales.The dynamics near the resonance band is revealed by doing a singular perturbation analysis and combining the extended Melnikov method.We are able to determine the criterion for the existence of the multi-pulse homoclinic orbits which can form the Shilnikov orbits and give rise to chaos.At last,numerical results are also given to illustrate the nonlinear behaviors and chaotic motions in the nonlinear nano-oscillator.展开更多
Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision,nonlinear interactions of gravity waves are simulated and the matching relationships of the wavelengths and frequencies of t...Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision,nonlinear interactions of gravity waves are simulated and the matching relationships of the wavelengths and frequencies of the interacting waves are discussed.In resonant interactions,the wavelengths of the excited wave are in good agreement with the values derived from sum or difference resonant conditions,and the frequencies of the three waves also satisfy the matching condition.Since the interacting waves obey the resonant conditions,resonant interactions have a reversible feature that for a resonant wave triad,any two waves are selected to be the initial perturbations,and the third wave can then be excited through sum or difference resonant interaction.The numerical results for nonresonant triads show that in nonresonant interactions,the wave vectors tend to approximately match in a single direction,generally in the horizontal direction.The frequency of the excited wave is close to the matching value,and the degree of mismatching of frequencies may depend on the combined effect of both the wavenumber and frequency mismatches that should benefit energy exchange to the greatest extent.The matching and mismatching relationships in nonresonant interactions differ from the results of weak interaction theory that the wave vectors are required to satisfy the resonant matching condition but the frequencies are permitted to mismatch and oscillate with amplitude of half the mismatching frequency.Nonresonant excitation has an irreversible characteristic,which is different from what is found for the resonant interaction.For specified initial primary and secondary waves,it is difficult to predict the values of the mismatching wavenumber and frequency for the excited wave owing to the complexity.展开更多
文摘Based on the structural and mechanics analysis of aero-engines rotor system, the dynamic model of the flexible rotor system with multi-supports are presented in order to solve the bearing misalignment problem of rotor system in aero-engines. The motion equations are derived through Lagrange method. The relationship between structural and mechanics characteristics parameters are built up. Finally, the dynamic influence of bearing misalignment on rotor system are divided into three kinds： additional rotor bending rigidity, additional bearing misalignment excitation force and additional imbalance. The equations suggest that additional imbalance excitation force activates the nonlinearity on rotor system and an additional 2x excitation force might appear.
基金supported by the National Natural Science Foundation of China (Grant No. 50538030)
文摘Urban trains running on ground surface lead to evironmental ground vibrations in the vicinity of railwaylines. The complicated vibration source of the system can hardly be measured directly. The inversion methodology in engineering seismology is borrowed here to study the dynamic exciting sourec, i.e., the wheel-rail unevenness. A dynamic coupled train-track-3D ground model is combined with a genetic algorithm for the inversion. The solution space of the inversion variables, the objective function and the solving genetic strategy of the inversion are determined, and a joint inversion for the wheel-rail unevenness source function and some track structure parameters is therefore designed. The wheel-rail unevenness PSD, being the source function of No. 13 Beijing urban railway, is obtained by the inversoin based on observed data in the field. The result indicates that the source function discribes the track unevenness in the range of wavelength over 1.2 m, and reflects properly wheel irregularites in the range of wavelength shorter than 1.2 m. It should be noticed that the urban rail traffic is not very fast, and this range of short wavelength is exactly corresponding to the main frequency band of environmental vibrations from the traffic. The unevenness of wavelength under 1.2 m is underestimated, and the ground vibration in the main frequency band must be underestimated consequently, if the track unevenness spectrum is taken as the source function. Rather than the track spectrum reflecting just the evenness of track, the wheel-rail spectrum expresses both the track unevenness and the irregularities of wheels, and therefore is more suitable to be the source function of urban railway traffic. It is also convinced that the exciting source inversion according to observed ground vibrations is an effective way to detect quantitatively the combined wheel-rail unevenness.
基金supported by the National Natural Science Foundation of China(Grant Nos.11290152,11072008 and 11372015)the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality(PHRIHLB)
文摘In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are studied.The damping,parametrical excitation and the nonlinearities are regarded as weak.The averaged equation depicting the fast and slow dynamics is derived through the method of multiple scales.The dynamics near the resonance band is revealed by doing a singular perturbation analysis and combining the extended Melnikov method.We are able to determine the criterion for the existence of the multi-pulse homoclinic orbits which can form the Shilnikov orbits and give rise to chaos.At last,numerical results are also given to illustrate the nonlinear behaviors and chaotic motions in the nonlinear nano-oscillator.
基金supported by National Natural Science Foundation of China (Grant Nos. 41074110,41174133 and 40825013)National Basic Research Program of China (Grant No. 2012CB825605)+2 种基金Ocean Public Welfare Scientific Research Project,State Oceanic Administration People’s Republic of China (Grant No. 201005017)China Meteorological Administration (Grant No. GYHY201106011)Fundamental Research Funds for the Central Universities
文摘Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision,nonlinear interactions of gravity waves are simulated and the matching relationships of the wavelengths and frequencies of the interacting waves are discussed.In resonant interactions,the wavelengths of the excited wave are in good agreement with the values derived from sum or difference resonant conditions,and the frequencies of the three waves also satisfy the matching condition.Since the interacting waves obey the resonant conditions,resonant interactions have a reversible feature that for a resonant wave triad,any two waves are selected to be the initial perturbations,and the third wave can then be excited through sum or difference resonant interaction.The numerical results for nonresonant triads show that in nonresonant interactions,the wave vectors tend to approximately match in a single direction,generally in the horizontal direction.The frequency of the excited wave is close to the matching value,and the degree of mismatching of frequencies may depend on the combined effect of both the wavenumber and frequency mismatches that should benefit energy exchange to the greatest extent.The matching and mismatching relationships in nonresonant interactions differ from the results of weak interaction theory that the wave vectors are required to satisfy the resonant matching condition but the frequencies are permitted to mismatch and oscillate with amplitude of half the mismatching frequency.Nonresonant excitation has an irreversible characteristic,which is different from what is found for the resonant interaction.For specified initial primary and secondary waves,it is difficult to predict the values of the mismatching wavenumber and frequency for the excited wave owing to the complexity.
