This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed ...This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed by using theoretical methods.It is shown that the sub-harmonic resonance may occur due to maneuvering flight conditions.The larger the eccentricity E and the maneuver load G,the greater the sub-harmonic resonance.The effects of nonlinear stiffness,damping of the system,maneuver load,and eccentricity on the sub-harmonic resonance region in parameter planes are also investigated.Bifurcation diagrams of the analytical solutions are in good agreement with that of the numerical simulation solutions.These results will contribute to the understanding of the nonlinear dynamic behaviors of maneuvering rotor systems.展开更多
The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the ave...The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.展开更多
With the development of wireless communication,the 6G mobile communication technology has received wide attention.As one of the key technologies of 6G,terahertz(THz)communication technology has the characteristics of ...With the development of wireless communication,the 6G mobile communication technology has received wide attention.As one of the key technologies of 6G,terahertz(THz)communication technology has the characteristics of ultra-high bandwidth,high security and low environmental noise.In this paper,a THz duplexer with a half-wavelength coupling structure and a sub-harmonic mixer operating at 216 GHz and 204 GHz are designed and measured.Based on these key devices,a 220 GHz frequency-division multiplexing communication system is proposed,with a real-time data rate of 10.4 Gbit/s for one channel and a transmission distance of 15 m.The measured constellation diagram of two receivers is clearly visible,the signal-to-noise ratio(SNR)is higher than 22 dB,and the bit error ratio(BER)is less than 10^(−8).Furthermore,the high definition(HD)4K video can also be transmitted in real time without stutter.展开更多
Sub-harmonic component generated from microbubbles is proven to be potentially used in noninvasive blood pressure measurement. Both theoretical and experimental studies are performed in the present work to investigate...Sub-harmonic component generated from microbubbles is proven to be potentially used in noninvasive blood pressure measurement. Both theoretical and experimental studies are performed in the present work to investigate the dependence of the sub-harmonic generation on the overpressure with different excitation pressure amplitudes and pulse lengths. With 4-MHz ultrasound excitation at an applied acoustic pressure amplitude of 0.24 MPa, the measured sub-harmonic amplitude exhibits a decreasing change as overpressure increases; while non-monotonic change is observed for the applied acoustic pressures of 0.36 MPa and 0.48 MPa, and the peak position in the curve of the sub-harmonic response versus the overpres- sure shifts toward higher overpressure as the excitation pressure amplitude increases. Furthermore, the exciting pulse with long duration could lead to a better sensitivity of the sub-harmonic response to overpressure. The measured results are ex- plained by the numerical simulations based on the Marmottant model. The numerical simulations qualitatively accord with the measured results. This work might provide a preliminary proof for the optimization of the noninvasive blood pressure measurement through using sub-harmonic generation from microbubbles.展开更多
Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also ...Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.展开更多
This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch mode...This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch modes, the coupled heave and pitch motion equations of the spar platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs were constructed, the Poincare maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to wave fre- quency. With changing wave frequency, the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. When the wave frequency approaches the natural frequency of the heave mode of the platform, the platform moves with quasi-periodic motion and chaotic motional temately. For a certain range of wave frequencies, the platform moves with totally chaotic motion. The range of wave frequencies which leads to chaotic motion of the platform increases with increasing wave height. The three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs reveal the nonlinear motions of the spar platform under different wave conditions.展开更多
Parabolized stability equations （PSE） approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether ...Parabolized stability equations （PSE） approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.展开更多
In this paper, we first define a kind of pseudo-distance function and annulus domain on Riemann surfaces, then prove the Hadamard Theorem and the Borel-Carathéodory Theorem on any Riemann surfaces.
An room temperature low noise anti-parallel Schottky diode based 630-720 GHz sub-harmonic mixer(SHM) is designed, built and measured. Intrinsic resonances in lowpass hammer-head filter have been adopted to prevent the...An room temperature low noise anti-parallel Schottky diode based 630-720 GHz sub-harmonic mixer(SHM) is designed, built and measured. Intrinsic resonances in lowpass hammer-head filter have been adopted to prevent the LO and RF power leak from the IF channel, while greatly minimizing the transmission line size. The mixer consists of 15 um quartz terahertz circuit and 127 um Al2 O3 IF transformer circuit. An improved lumped element equivalent noise model of SBDs guarantees the accuracy of simulation. The measurement indicates that with local oscillating(LO)signal of 2-8 mW, the lowest double sideband(DSB) conversion loss is 8.2 dB at 645 GHz,and the best DSB noise temperature is 2800 K at 657 GHz. The 3 dB bandwidth of conversion loss is 75 GHz from 638 to 715 GHz. The work IF frequency band is above 20 GHz ranging from 1 to 20 GHz with-10 dB return loss.展开更多
In order to improve the bandwidth of the conventional sub-harmonic mixer, a broad-band, high intermediate frequency（IF） sub-harmonic mixer for W-band applications is proposed. Replacing the open and short stubs that...In order to improve the bandwidth of the conventional sub-harmonic mixer, a broad-band, high intermediate frequency（IF） sub-harmonic mixer for W-band applications is proposed. Replacing the open and short stubs that are used in the convertional sub-harmonic mixer with a broad-band band-pass filter and a low-pass filter, respectively, a wide operating frequency band is achieved. Furthermore, without the use of the edge-coupled band-pass filter at radio frequency（RF） port, the proposed structure can be realized by common hybrid microwave integrated circuit technology at W- band. The measured results show that the proposed subharmonic mixer can operate from 80 to 107.5 GHz for RF frequency and support up to 18 GHz for the IF bandwidth. Also, the measured results show that the single-sideband conversion loss is less than 13. 7 dB over the available RF frequency band, while the minimum conversion loss is about 9 dB at an RF of 92. 5 GHz and an 1F of 3 GHz. Thus, a large operating bandwidth performance at W-band can be achieved by the orooosed mixer.展开更多
Dielectric elastomers have found interesting applications in soft loudspeakers,where vibrations subject to alternating electrical excitations are the key features.Although there are many t heore tical studies on the n...Dielectric elastomers have found interesting applications in soft loudspeakers,where vibrations subject to alternating electrical excitations are the key features.Although there are many t heore tical studies on the nonlinear vibrations of dielec trie elasto mers subject to electromechanical coupling loads,the systematic experimental research is rare.In this work,we design a simple experimental setup to observe the out-of-plane vibrations of a circular dielec trie elastomer actuator.We find that the dielec trie elastomer has different response modes including the harmonic,super-harmonic and sub-harmonic responses at different excitation frequencies.We analyze the responses by using the short-time Fourier transformation.We find that the equivalent voltage and the AC/DC ratio are the main parameters affecting the occurrence of sub-harmonic responses.The phenomenon of mode shift is also observed in our experiments.These experimental observations provide a deeper unders tanding of the dynamic responses of dielec trie elasto mer subject to electromechanical loads.展开更多
During the design process, multipacting effect has been taken into consideration using a 2D simulation code MultiPac and all of the corners are rounded to suppress the multipacting effect in the pill-box cavity. Howev...During the design process, multipacting effect has been taken into consideration using a 2D simulation code MultiPac and all of the corners are rounded to suppress the multipacting effect in the pill-box cavity. However, unexpected multipacting effect prevents the increase of the input power when the magnetic field of focusing coils is added after adequate conditioning and a novel method is adopted to suppress it by introducing extra coils to counteract the field. This paper focuses on the simulation of multipacting effect in different magnetic field configurations. The experimental observations and simulation results of multipacting effect are presented and details of the multipacting process are also analyzed.展开更多
This paper presents the design and simulation of several fixed-tuned sub-harmonic mixers cover frequencies from 110 GH to 130 GHz, 215 GH to 235 GHz, 310 GH to 350 GHz, and 400 GH to 440 GHz. Among them, 120 GHz, 225 ...This paper presents the design and simulation of several fixed-tuned sub-harmonic mixers cover frequencies from 110 GH to 130 GHz, 215 GH to 235 GHz, 310 GH to 350 GHz, and 400 GH to 440 GHz. Among them, 120 GHz, 225 GHz, 330 GHz subharmonic mixers are designed with flip-chipped planar schottky diode mounted onto a suspended quartz-based substrate, the 225 GHz and 425 GHz subharmonic mixers are GaAs membrane integrated, and the 115 GHz subharmonic mixer has been fabricated and tested already.展开更多
The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-har...The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.展开更多
The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small param...The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small parameters, which do not exist in most practical systems. Those methods are limited in dealing with the systems with strong nonlinearities. This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used to extend the Melnikov functions to the strongly nonlinear systems. Applied to a given example, the procedure shows the effectiveness via the comparison of the theoretical results and the numerical simulation.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10632040)
文摘This paper focuses on the 1/2 sub-harmonic resonance of an aircraft’s rotor system under hovering flight that can be modeled as a maneuver load G in the equations of motion.The effect on the rotor system is analyzed by using theoretical methods.It is shown that the sub-harmonic resonance may occur due to maneuvering flight conditions.The larger the eccentricity E and the maneuver load G,the greater the sub-harmonic resonance.The effects of nonlinear stiffness,damping of the system,maneuver load,and eccentricity on the sub-harmonic resonance region in parameter planes are also investigated.Bifurcation diagrams of the analytical solutions are in good agreement with that of the numerical simulation solutions.These results will contribute to the understanding of the nonlinear dynamic behaviors of maneuvering rotor systems.
文摘The quasi-periodic perturbation for the Duffing's equation with two external forcing terms has been discussed. The second order averaging method and sub-harmonic Melnikov's method through the medium of the averaging mrthod have been applied to detect the existence of quasiperiodic solutions and sub-harmonic bifurcation for the system. Sub-harmonic bifurcation curves are given by using numerical computation for sub-harmonic Melnikov's function.
基金supported by the National Natural Science Foundation of China under Grant Nos.62022022 and 62101107the National Key R&D Program of China under Grant No.2018YFB1801502+1 种基金China Postdoctoral Science Foundation under Grant No.2021TQ0057ZTE Industry-Uni⁃versity-Institute Cooperation Funds.
文摘With the development of wireless communication,the 6G mobile communication technology has received wide attention.As one of the key technologies of 6G,terahertz(THz)communication technology has the characteristics of ultra-high bandwidth,high security and low environmental noise.In this paper,a THz duplexer with a half-wavelength coupling structure and a sub-harmonic mixer operating at 216 GHz and 204 GHz are designed and measured.Based on these key devices,a 220 GHz frequency-division multiplexing communication system is proposed,with a real-time data rate of 10.4 Gbit/s for one channel and a transmission distance of 15 m.The measured constellation diagram of two receivers is clearly visible,the signal-to-noise ratio(SNR)is higher than 22 dB,and the bit error ratio(BER)is less than 10^(−8).Furthermore,the high definition(HD)4K video can also be transmitted in real time without stutter.
基金Project supported by the National Basic Research Program from Ministry of Science and Technology,China(Grant No.2011CB707900)the National Natural Science Foundation of China(Grant Nos.81271589,81227004,11174141,11374155,11612032,and 81301616)the Natural Science Foundation of Jiangsu Province,China(Grant Nos.BE2011110 and BK20131017)
文摘Sub-harmonic component generated from microbubbles is proven to be potentially used in noninvasive blood pressure measurement. Both theoretical and experimental studies are performed in the present work to investigate the dependence of the sub-harmonic generation on the overpressure with different excitation pressure amplitudes and pulse lengths. With 4-MHz ultrasound excitation at an applied acoustic pressure amplitude of 0.24 MPa, the measured sub-harmonic amplitude exhibits a decreasing change as overpressure increases; while non-monotonic change is observed for the applied acoustic pressures of 0.36 MPa and 0.48 MPa, and the peak position in the curve of the sub-harmonic response versus the overpres- sure shifts toward higher overpressure as the excitation pressure amplitude increases. Furthermore, the exciting pulse with long duration could lead to a better sensitivity of the sub-harmonic response to overpressure. The measured results are ex- plained by the numerical simulations based on the Marmottant model. The numerical simulations qualitatively accord with the measured results. This work might provide a preliminary proof for the optimization of the noninvasive blood pressure measurement through using sub-harmonic generation from microbubbles.
基金supported by the National Natural Science Foundation of China(Grant No.51279130)
文摘Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.
基金supported by the National Natural Science Foundation of China under Grant No.51179125the Innovation Foundation of Tianjin University under Approving No.1301
文摘This paper presents the results from a numerical study on the nonlinear dynamic behaviors including bifurcation and chaos of a truss spar platform. In view of the mutual influences between the heave and the pitch modes, the coupled heave and pitch motion equations of the spar platform hull were established in the regular waves. In order to analyze the nonlinear motions of the platform, three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs were constructed, the Poincare maps and the power spectrums of the platform response were calculated. It was found that the platform motions are sensitive to wave fre- quency. With changing wave frequency, the platform undergoes complicated nonlinear motions, including 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. When the wave frequency approaches the natural frequency of the heave mode of the platform, the platform moves with quasi-periodic motion and chaotic motional temately. For a certain range of wave frequencies, the platform moves with totally chaotic motion. The range of wave frequencies which leads to chaotic motion of the platform increases with increasing wave height. The three-dimensional maximum Lyapunov exponent graphs and the bifurcation graphs reveal the nonlinear motions of the spar platform under different wave conditions.
基金Project supported by the National Natural Science Foundation of China(Nos.10632050,90716007)the Foundation of LIU Hui Center of Applied Mathematics of Nankai University and Tianjin University
文摘Parabolized stability equations （PSE） approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.
文摘In this paper, we first define a kind of pseudo-distance function and annulus domain on Riemann surfaces, then prove the Hadamard Theorem and the Borel-Carathéodory Theorem on any Riemann surfaces.
基金supported by National Key Basic Research Program of China (grant No.2015CB755406)
文摘An room temperature low noise anti-parallel Schottky diode based 630-720 GHz sub-harmonic mixer(SHM) is designed, built and measured. Intrinsic resonances in lowpass hammer-head filter have been adopted to prevent the LO and RF power leak from the IF channel, while greatly minimizing the transmission line size. The mixer consists of 15 um quartz terahertz circuit and 127 um Al2 O3 IF transformer circuit. An improved lumped element equivalent noise model of SBDs guarantees the accuracy of simulation. The measurement indicates that with local oscillating(LO)signal of 2-8 mW, the lowest double sideband(DSB) conversion loss is 8.2 dB at 645 GHz,and the best DSB noise temperature is 2800 K at 657 GHz. The 3 dB bandwidth of conversion loss is 75 GHz from 638 to 715 GHz. The work IF frequency band is above 20 GHz ranging from 1 to 20 GHz with-10 dB return loss.
基金Research Foundation of China ( No.9140A01020209JW0601)
文摘In order to improve the bandwidth of the conventional sub-harmonic mixer, a broad-band, high intermediate frequency（IF） sub-harmonic mixer for W-band applications is proposed. Replacing the open and short stubs that are used in the convertional sub-harmonic mixer with a broad-band band-pass filter and a low-pass filter, respectively, a wide operating frequency band is achieved. Furthermore, without the use of the edge-coupled band-pass filter at radio frequency（RF） port, the proposed structure can be realized by common hybrid microwave integrated circuit technology at W- band. The measured results show that the proposed subharmonic mixer can operate from 80 to 107.5 GHz for RF frequency and support up to 18 GHz for the IF bandwidth. Also, the measured results show that the single-sideband conversion loss is less than 13. 7 dB over the available RF frequency band, while the minimum conversion loss is about 9 dB at an RF of 92. 5 GHz and an 1F of 3 GHz. Thus, a large operating bandwidth performance at W-band can be achieved by the orooosed mixer.
文摘Dielectric elastomers have found interesting applications in soft loudspeakers,where vibrations subject to alternating electrical excitations are the key features.Although there are many t heore tical studies on the nonlinear vibrations of dielec trie elasto mers subject to electromechanical coupling loads,the systematic experimental research is rare.In this work,we design a simple experimental setup to observe the out-of-plane vibrations of a circular dielec trie elastomer actuator.We find that the dielec trie elastomer has different response modes including the harmonic,super-harmonic and sub-harmonic responses at different excitation frequencies.We analyze the responses by using the short-time Fourier transformation.We find that the equivalent voltage and the AC/DC ratio are the main parameters affecting the occurrence of sub-harmonic responses.The phenomenon of mode shift is also observed in our experiments.These experimental observations provide a deeper unders tanding of the dynamic responses of dielec trie elasto mer subject to electromechanical loads.
文摘During the design process, multipacting effect has been taken into consideration using a 2D simulation code MultiPac and all of the corners are rounded to suppress the multipacting effect in the pill-box cavity. However, unexpected multipacting effect prevents the increase of the input power when the magnetic field of focusing coils is added after adequate conditioning and a novel method is adopted to suppress it by introducing extra coils to counteract the field. This paper focuses on the simulation of multipacting effect in different magnetic field configurations. The experimental observations and simulation results of multipacting effect are presented and details of the multipacting process are also analyzed.
基金supported by the National Natural Science Foundation of China under Grant No.61301051
文摘This paper presents the design and simulation of several fixed-tuned sub-harmonic mixers cover frequencies from 110 GH to 130 GHz, 215 GH to 235 GHz, 310 GH to 350 GHz, and 400 GH to 440 GHz. Among them, 120 GHz, 225 GHz, 330 GHz subharmonic mixers are designed with flip-chipped planar schottky diode mounted onto a suspended quartz-based substrate, the 225 GHz and 425 GHz subharmonic mixers are GaAs membrane integrated, and the 115 GHz subharmonic mixer has been fabricated and tested already.
基金Project supported by the National Natural Science Foundation of China (No.50275024)
文摘The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.
基金Project supported by the National Natural Science Foundation of China(No.10632040)
文摘The Melnikov method is important for detecting the presence of transverse homoclinic orbits and the occurrence of homoclinic bifurcations. Unfortunately, the traditional Melnikov methods strongly depend on small parameters, which do not exist in most practical systems. Those methods are limited in dealing with the systems with strong nonlinearities. This paper presents a procedure to study the chaos and sub-harmonic resonance of strongly nonlinear practical systems by employing a homotopy method that is used to extend the Melnikov functions to the strongly nonlinear systems. Applied to a given example, the procedure shows the effectiveness via the comparison of the theoretical results and the numerical simulation.
