Spray deposit distribution from a field sprayer is mainly affected by the boom movements when the tractor is driven over a rough soil surface,the pendulum suspension that used to reduce and control the movement of spr...Spray deposit distribution from a field sprayer is mainly affected by the boom movements when the tractor is driven over a rough soil surface,the pendulum suspension that used to reduce and control the movement of spray boom by isolating the boom from vibrations of the tractor will directly enhance uniform deposition of chemicals.However,how to match the parameters of the suspension with the properties of the boom is the key problem.The dynamic rigid-flexible coupling model of the virtual prototype of the spray boom suspension system was established by using ADAMS and ABAQUS software.An optimization of the suspension parameters for a large spay boom was carried out based on the optimal Latin hypercube design,radial basis function neural network,and multi-objective genetic algorithm NSGA-II.After modified parameters of the suspension,the travel of the sprayer on a typical field motion track was simulated based on a six DOF motion simulator,and the dynamic behavior of the boom suspension was measured.The results show that RMS of the measured boom roll angle and the boom center displacement for optimized solution were reduced by 14.76%and 12.43%compared with the original suspension.Finally,the inertial measurement unit(IMU)was used to measure the movements of the sprayer vehicle during the pesticide application on the Hongze Lake Farm,the experiment of field condition reproduced by using the six DOF motion simulator,the standard deviation of the roll angle and vibration displacement for the optimized sprayer boom are only 0.6382°and 62.279 mm respectively.The research provides theoretical basis and experimental method for parameter optimization of large scale boom suspension.展开更多
The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order avera...The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov＇s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω ＋ εv, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f0 and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from period- one orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven＇t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.展开更多
This paper is a continuation of ＂Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations＂[1].In this paper,we investigate the existence and the bifurcations of resonant solution for ω0：ω：...This paper is a continuation of ＂Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations＂[1].In this paper,we investigate the existence and the bifurcations of resonant solution for ω0：ω：Ω ≈ 1：1：n,1：2：n,1：3：n,2：1：n and 3：1：n by using second-order averaging method,give a criterion for the existence of resonant solution for ω0：ω：Ω ≈ 1：m：n by using Melnikov＇s method and verify the theoretical analysis by numerical simulations.By numerical simulation,we expose some other interesting dynamical behaviors including the entire invariant torus region,the cascade of invariant torus behaviors,the entire chaos region without periodic windows,chaotic region with complex periodic windows,the entire period-one orbits region;the jumping behaviors including invariant torus behaviors converting to period-one orbits,from chaos to invariant torus behaviors or from invariant torus behaviors to chaos,from period-one to chaos,from invariant torus behaviors to another invariant torus behaviors;the interior crisis;and the different nice invariant torus attractors and chaotic attractors.The numerical results show the difference of dynamical behaviors for the physical pendulum equation with suspension axis vibrations between the cases under the three frequencies resonant condition and under the periodic/quasi-periodic perturbations.It exhibits many invariant torus behaviors under the resonant conditions.We find a lot of chaotic behaviors which are different from those under the periodic/quasi-periodic perturbations.However,we did not find the cascades of period-doubling bifurcation.展开更多
基金This study was financially supported by the National Key Research and Development Program of China(2016YFD0200705)the National Natural Science Foundation of China(Grant No.51605236)the Independent Innovation Fund of Agricultural Science and Technology of Jiangsu Province(CX(16)1043).
文摘Spray deposit distribution from a field sprayer is mainly affected by the boom movements when the tractor is driven over a rough soil surface,the pendulum suspension that used to reduce and control the movement of spray boom by isolating the boom from vibrations of the tractor will directly enhance uniform deposition of chemicals.However,how to match the parameters of the suspension with the properties of the boom is the key problem.The dynamic rigid-flexible coupling model of the virtual prototype of the spray boom suspension system was established by using ADAMS and ABAQUS software.An optimization of the suspension parameters for a large spay boom was carried out based on the optimal Latin hypercube design,radial basis function neural network,and multi-objective genetic algorithm NSGA-II.After modified parameters of the suspension,the travel of the sprayer on a typical field motion track was simulated based on a six DOF motion simulator,and the dynamic behavior of the boom suspension was measured.The results show that RMS of the measured boom roll angle and the boom center displacement for optimized solution were reduced by 14.76%and 12.43%compared with the original suspension.Finally,the inertial measurement unit(IMU)was used to measure the movements of the sprayer vehicle during the pesticide application on the Hongze Lake Farm,the experiment of field condition reproduced by using the six DOF motion simulator,the standard deviation of the roll angle and vibration displacement for the optimized sprayer boom are only 0.6382°and 62.279 mm respectively.The research provides theoretical basis and experimental method for parameter optimization of large scale boom suspension.
基金Supported by the National Natural Science Foundation of China(No.10671063)
文摘The physical pendulum equation with suspension axis vibrations is investigated. By using Melnikov＇s method, we prove the conditions for the existence of chaos under periodic perturbations. By using second-order averaging method and Melinikov＇s method, we give the conditions for the existence of chaos in an averaged system under quasi-periodic perturbations for Ω = nω ＋ εv, n = 1 - 4, where ν is not rational to ω. We are not able to prove the existence of chaos for n = 5 - 15, but show the chaotic behavior for n = 5 by numerical simulation. By numerical simulation we check on our theoretical analysis and further exhibit the complex dynamical behavior, including the bifurcation and reverse bifurcation from period-one to period-two orbits; the onset of chaos, the entire chaotic region without periodic windows, chaotic regions with complex periodic windows or with complex quasi-periodic windows; chaotic behaviors suddenly disappearing, or converting to period-one orbit which means that the system can be stabilized to periodic motion by adjusting bifurcation parameters α, δ, f0 and Ω; and the onset of invariant torus or quasi-periodic behaviors, the entire invariant torus region or quasi-periodic region without periodic window, quasi-periodic behaviors or invariant torus behaviors suddenly disappearing or converting to periodic orbit; and the jumping behaviors which including from period- one orbit to anther period-one orbit, from quasi-periodic set to another quasi-periodic set; and the interleaving occurrence of chaotic behaviors and invariant torus behaviors or quasi-periodic behaviors; and the interior crisis; and the symmetry breaking of period-one orbit; and the different nice chaotic attractors. However, we haven＇t find the cascades of period-doubling bifurcations under the quasi-periodic perturbations and show the differences of dynamical behaviors and technics of research between the periodic perturbations and quasi-periodic perturbations.
基金Supported by the National Natural Science Foundation of China (No.10671063 and 10801135)
文摘This paper is a continuation of ＂Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations＂[1].In this paper,we investigate the existence and the bifurcations of resonant solution for ω0：ω：Ω ≈ 1：1：n,1：2：n,1：3：n,2：1：n and 3：1：n by using second-order averaging method,give a criterion for the existence of resonant solution for ω0：ω：Ω ≈ 1：m：n by using Melnikov＇s method and verify the theoretical analysis by numerical simulations.By numerical simulation,we expose some other interesting dynamical behaviors including the entire invariant torus region,the cascade of invariant torus behaviors,the entire chaos region without periodic windows,chaotic region with complex periodic windows,the entire period-one orbits region;the jumping behaviors including invariant torus behaviors converting to period-one orbits,from chaos to invariant torus behaviors or from invariant torus behaviors to chaos,from period-one to chaos,from invariant torus behaviors to another invariant torus behaviors;the interior crisis;and the different nice invariant torus attractors and chaotic attractors.The numerical results show the difference of dynamical behaviors for the physical pendulum equation with suspension axis vibrations between the cases under the three frequencies resonant condition and under the periodic/quasi-periodic perturbations.It exhibits many invariant torus behaviors under the resonant conditions.We find a lot of chaotic behaviors which are different from those under the periodic/quasi-periodic perturbations.However,we did not find the cascades of period-doubling bifurcation.
