Enhancing suspension vibration reduction by diagonal inerter

The diagonal inerter is integrated into a suspension vibration reduction system(SVRS).The dynamic model of the SVRS with diagonal inerter and damping is established.The dynamic model is of strong geometric nonlinearity.The retaining nonlinearity up to cubic terms is validated under impact excitation.The conditions omitting the static deformation are determined.The effects of the diagonal inerter on the vibration reduction performance of the SVRS are explored under impact and random excitations.The vibration reduction performance of the proposed SVRS with both diagonal inerter and damping is better than that of either the SVRS without them or the SVRS with the diagonal damping only.

Complex Dynamics in Physical Pendulum Equation with Suspension Axis Vibrations

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.

Bifurcations of Resonant Solutions and Chaos in Physical Pendulum Equation with Suspension Axis Vibrations

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.

正弦激励下三磁铁磁悬浮动力吸振器的被动减振性能研究

本本文设计了一种新型的三磁铁磁悬浮动力吸振器(TMSDVA),并进行了建模和测试首先建立了TMSDVA悬臂梁减振系统的等效动力学模型.基于等效磁化电流理论,建立了非线性磁悬浮力的计算模型,并分析了非线性磁悬浮力的特征.然后用Runge-Kutta方法求解系统在正弦激励下的动力学响应.通过对仿真结果的分析发现,适当调整TMSDVA的阻尼系数不仅可以降低TMSDVA的减振效果对激励幅值的敏感性,还可以整体提高TMSDVA的减振效果.最后通过实验验证了理论分析的正确性.综合来看,TMSDVA在工程结构的被动减振方面具有潜在应用价值.