Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. T...Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.展开更多
To improve the quality of ultrasonic elastography, by taking the advantage of code excitation and frequency compounding, a transmitting-side multi-frequency with coded excitation for elastography （TFCCE） was propose...To improve the quality of ultrasonic elastography, by taking the advantage of code excitation and frequency compounding, a transmitting-side multi-frequency with coded excitation for elastography （TFCCE） was proposed. TFCCE adopts the chirp signal excitation scheme and strikes a balance in the selection of sub-signal bandwidth, the bandwidth overlap and the number of sub-strain image based on theoretical derivation, so as to further improve the quality of elastic image. Experiments have proved that, compared with the other optimizing methods, the elastographyic signal-to-noise ratio（Re-SN） and contrast-to-noise ratio（Re-CN） are improved significantly with different echo signal-to-noise ratios （ReSN） and attenuation coefficients. When ReSN is 50 dB, compared with short pulse, Rc-SN and Re-CN obtained by TFCCE increase by 53% and 143%, respectively. Moreover, in a deeper investigation （85-95 mm）, the image has lower strain noise and clear details. When the attenuation coefficient is in the range of 0-1 dB/（cm.MHz）, Re-SN and Re-CN obtained by TFCCE can be kept in moderate ranges of 5〈Re-SN〈6.8 and 11.4〈Re-CN〈15.2, respectively. In particular, for higher tissue attenuation, the basic image quality cannot be ensured with short pulse excitation, while mediocre quality strain figure can be obtained by TFCCE. Therefore, the TFCCE technology can effectively improve the elastography quality and can be applied to ultrasonic clinical trials.展开更多
The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincaré map...The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincaré map, the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied. The (Melnikov's) global perturbation technique was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.展开更多
The“synchronous impact”is a phenomenon that increases the dynamic load of the inter-shaft bearing,when the frequency of the aerodynamic excitation is close to the contact frequency of the inter-shaft bearing.This wo...The“synchronous impact”is a phenomenon that increases the dynamic load of the inter-shaft bearing,when the frequency of the aerodynamic excitation is close to the contact frequency of the inter-shaft bearing.This work addresses the“synchronous impact”phenomenon of an aero-engine.The 104 degree-of-freedom dynamical model of an aero-engine is established by the finite element method,in which the complex nonlinearity of the Hertzian contact force of the inter-shaft bearing with clearance is included,and the multi-frequency excitations such as the unbalanced excitations of the high-and low-pressure rotors and the aerodynamic excitation are considered.A harmonic balance method combined with the alternating frequency time-domain method(HB-AFT)is introduced to obtain periodic responses of the high-dimension complex nonlinear dual-rotor system.The results show that there emerges a peak value of the amplitude-frequency response for the contact frequency harmonic component of the outer ring of the inter-shaft bearing,when the aerodynamic excitation frequency is close to the contact frequency.In addition,the dynamic load of the inter-shaft bearing increases significantly.Moreover,the parametric analysis shows that the“synchronous impact”phenomenon is sensitive to the change of the speed ratio of the high-and low-pressure rotors.The dynamic load of inter-shaft bearing can be significantly reduced by changing the speed ratio by 1%.The results obtained in this paper not only provide more insight into the mechanism of the“synchronous impact”phenomenon but also demonstrate the HBAFT method as a potential semi-analytical tool to explore the high-dimension complex nonlinear system.展开更多
The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The a...The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.展开更多
The prompt fission neutron spectra for the neutron-induced fission of 233U for low energy neutrons （below 6 MeV） are calculated using nuclear evaporation theory with a semi-empirical method, in which the partition o...The prompt fission neutron spectra for the neutron-induced fission of 233U for low energy neutrons （below 6 MeV） are calculated using nuclear evaporation theory with a semi-empirical method, in which the partition of the total excitation energy between the fission fragments for the nth＋233U fission reactions is determined by the available experimental and evaluation data. The calculated prompt fission neutron spectra agree well with the experimental data. The proportions of high-energy neutrons of prompt fission neutron spectrum versus incident neutron energies are investigated with the theoretical spectra, and the results are consistent with the systematics. The semi-empirical method could be a useful tool for the prompt evaluation of fission neutron spectra.展开更多
For the n＋235U fission reaction, the total excitation energy partition of the fission fragments, the average neutron kinetic energy ε （A） and the total average energies Eˉγ（A） removed by γ rays as a function ...For the n＋235U fission reaction, the total excitation energy partition of the fission fragments, the average neutron kinetic energy ε （A） and the total average energies Eˉγ（A） removed by γ rays as a function of fission fragment mass are given at incident energies up to 20 MeV. The prompt neutron multiplicity as a function of the fragment mass, ν（A）, for neutron-induced fission of 235U at different incident neutron energies is calculated. The calculated results are checked with the total average prompt neutron multiplicities νˉ and compared with the experimental and evaluated data. Some prompt neutron and γ emission mechanisms are discussed.展开更多
文摘Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.
基金Project(2013GZX0147-3) supported by the Natural Science Foundation of Sichuan Province,China
文摘To improve the quality of ultrasonic elastography, by taking the advantage of code excitation and frequency compounding, a transmitting-side multi-frequency with coded excitation for elastography （TFCCE） was proposed. TFCCE adopts the chirp signal excitation scheme and strikes a balance in the selection of sub-signal bandwidth, the bandwidth overlap and the number of sub-strain image based on theoretical derivation, so as to further improve the quality of elastic image. Experiments have proved that, compared with the other optimizing methods, the elastographyic signal-to-noise ratio（Re-SN） and contrast-to-noise ratio（Re-CN） are improved significantly with different echo signal-to-noise ratios （ReSN） and attenuation coefficients. When ReSN is 50 dB, compared with short pulse, Rc-SN and Re-CN obtained by TFCCE increase by 53% and 143%, respectively. Moreover, in a deeper investigation （85-95 mm）, the image has lower strain noise and clear details. When the attenuation coefficient is in the range of 0-1 dB/（cm.MHz）, Re-SN and Re-CN obtained by TFCCE can be kept in moderate ranges of 5〈Re-SN〈6.8 and 11.4〈Re-CN〈15.2, respectively. In particular, for higher tissue attenuation, the basic image quality cannot be ensured with short pulse excitation, while mediocre quality strain figure can be obtained by TFCCE. Therefore, the TFCCE technology can effectively improve the elastography quality and can be applied to ultrasonic clinical trials.
文摘The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincaré map, the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied. The (Melnikov's) global perturbation technique was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.
基金supported by the National Natural Science Foundation of China(Grant No.11972129)the National Major Science and Technology Projects of China(Grant No.2017-IV-0008-0045)+1 种基金Department of Science&Technology of Liaoning Province(Grant No.2019BS182)the Educational Department of Liaoning Province(Grant No.LJGD2019009)。
文摘The“synchronous impact”is a phenomenon that increases the dynamic load of the inter-shaft bearing,when the frequency of the aerodynamic excitation is close to the contact frequency of the inter-shaft bearing.This work addresses the“synchronous impact”phenomenon of an aero-engine.The 104 degree-of-freedom dynamical model of an aero-engine is established by the finite element method,in which the complex nonlinearity of the Hertzian contact force of the inter-shaft bearing with clearance is included,and the multi-frequency excitations such as the unbalanced excitations of the high-and low-pressure rotors and the aerodynamic excitation are considered.A harmonic balance method combined with the alternating frequency time-domain method(HB-AFT)is introduced to obtain periodic responses of the high-dimension complex nonlinear dual-rotor system.The results show that there emerges a peak value of the amplitude-frequency response for the contact frequency harmonic component of the outer ring of the inter-shaft bearing,when the aerodynamic excitation frequency is close to the contact frequency.In addition,the dynamic load of the inter-shaft bearing increases significantly.Moreover,the parametric analysis shows that the“synchronous impact”phenomenon is sensitive to the change of the speed ratio of the high-and low-pressure rotors.The dynamic load of inter-shaft bearing can be significantly reduced by changing the speed ratio by 1%.The results obtained in this paper not only provide more insight into the mechanism of the“synchronous impact”phenomenon but also demonstrate the HBAFT method as a potential semi-analytical tool to explore the high-dimension complex nonlinear system.
基金Project supported by the National Natural Science Foundation of China(Nos.11972129 and12372008)the National Major Science and Technology Projects of China(No.2017-IV-0008-0045)+3 种基金the Natural Science Foundation of Heilongjiang Province of China(No.YQ2022A008)the Fundamental Research Funds for the Central Universities of China(No.HIT.OCEF.2023006)the Polish National Science Centre of Poland under the OPUS 18 grant(No.2019/35/B/ST8/00980)the Tianjin University Independent Innovation Foundation of China(No.2023XJS-0038)。
文摘The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.
基金Supported by National Natural Science Foundation of China(11205246,91126010,91226102)
文摘The prompt fission neutron spectra for the neutron-induced fission of 233U for low energy neutrons （below 6 MeV） are calculated using nuclear evaporation theory with a semi-empirical method, in which the partition of the total excitation energy between the fission fragments for the nth＋233U fission reactions is determined by the available experimental and evaluation data. The calculated prompt fission neutron spectra agree well with the experimental data. The proportions of high-energy neutrons of prompt fission neutron spectrum versus incident neutron energies are investigated with the theoretical spectra, and the results are consistent with the systematics. The semi-empirical method could be a useful tool for the prompt evaluation of fission neutron spectra.
文摘For the n＋235U fission reaction, the total excitation energy partition of the fission fragments, the average neutron kinetic energy ε （A） and the total average energies Eˉγ（A） removed by γ rays as a function of fission fragment mass are given at incident energies up to 20 MeV. The prompt neutron multiplicity as a function of the fragment mass, ν（A）, for neutron-induced fission of 235U at different incident neutron energies is calculated. The calculated results are checked with the total average prompt neutron multiplicities νˉ and compared with the experimental and evaluated data. Some prompt neutron and γ emission mechanisms are discussed.
