非线性振动分析的均向量场法

通过构造向量形式的振动微分方程组，利用均向量场（AVF）法得到振动响应的向量差分迭代格式.该离散格式能够保能量，同时具有二阶精度的特征，从而给出非线性振动问题的均向量场法.介绍了均向量场法的基本步骤.在建立AVF格式时，对于微分方程中若干常见的项，直接给出相应的映射项.应用均向量场法研究了非线性单摆问题和Kepler(开普勒)问题，数值结果说明了该方法保能量和具有长时间求解能力的特性.     

边界输入输出结构下非线性梁光滑解的存在性(英文)

本文研究一个描述梁振动的非线性模型,其非线性由物理条件(Hooke律)导致,主要研究该模型在边界输入输出结构下局部光滑解的存在性.首先应用发展方程理论证明相关线性系统存在光滑解,然后由一系列能量估计结合不动点定理证明所考察的非线性系统局部光滑解的存在性.     

附加非线性振子的双稳态电磁式振动能量捕获器动力学特性研究

随着微机电科技的进步,利用环境振动进行系统自供电已经成为目前非线性动力学研究的热点.将质量-弹簧-阻尼系统与双稳态振动能量捕获系统相结合,提出了附加非线性振子的双稳态电磁式振动能量捕获器,建立系统的力学模型及控制方程.通过数值仿真研究了简谐激励下质量比和调频比发生变化时附加非线性振子的双稳态电磁式振动能量捕获器的动力学响应.通过与附加线性振子双稳态系统的对比,获得了上述参数对附加非线性振子的双稳态电磁式振动能量捕获器发生大幅运动的影响规律,显示出附加非线性振子的双稳态电磁式振动能量捕获器的优越性,并获得了附加非线性振子的双稳态电磁式振动能量捕获器发生连续大幅混沌运动的最优参数配合.上述研究结果为双稳态电磁式振动能量捕获系统的相关研究提供了理论基础.     

磁振子压电能量采集器的多尺度分析

根据磁振子压电能量采集器实验系统的数学模型,基于系统静平衡位形,引入坐标变换,建立相对位移的标准控制方程.利用Taylor级数展开法处理磁力非线性项,运用多尺度法近似解析分析,通过消除长期项获得可解性条件,并由此推导出稳态响应时的幅频关系.四阶Runge-Kutta方法用于数值计算受迫振动时间历程,数值算例给出了系统前两阶主共振下的稳态幅频响应关系及其失稳区域.结果表明多尺度方法所得到的一致有效解具有较高精度,可以为优化设计磁振子压电能量采集器提供理论依据.     

智能空间刚架的模糊自抗扰振动抑制研究

智能空间刚架作为太空望远镜支撑架是一种新型智能空间结构.为抑制刚架系统在运动过程中产生的振动,"文章提出了一种基于自抗扰控制的非线性模糊自抗扰控制理论,并设计出模糊自抗扰控制器.首先采用有限元方法计算出空间刚架的质量矩阵、阻尼矩阵和刚度矩阵,进而建立系统模型并设计出自抗扰控制器以实现对系统振动的抑制.基于普通自抗扰控制器,利用模糊推理在线整定控制器中非线性状态误差反馈的参数.该控制器不依赖于被控对象的精确数学模型,具有良好的控制性能,同时参数的在线自整定简化了调参难度.仿真实验验证了所提方法的有效性.     

随机激励下一类含分数阶阻尼的轮胎的振动响应

基于随机平均法研究了Kanai-Tajimi噪声激励下含分数阶阻尼的轮胎动力学系统的响应.首先将地震波近似为Kanai-Tajimi噪声,结合点接触模型和分数阶导数模型,建立轮胎的动力学方程,然后运用随机平均法求解振动位移的稳态概率密度函数的解析解,最后通过Monte-Carlo数值模拟验证了该方法的有效性.利用振动位移的概率密度求解聚丁二烯橡胶、丁基B252橡胶轮胎振动位移的均值与方差,并以此为依据考察这两类橡胶的减振性能.研究结果表明,轮胎振动位移的均值和方差随橡胶的储能模量的增大而增大,随耗散模量的增大而减小,这说明减小橡胶的储能模量或增大耗散模量可有效改善轮胎的减振性能.所得结果可为轮胎的设计与制造提供一定的理论基础.     

基于数据驱动方法的控制器设计及其参数整定

以一般离散时间非线性系统为研究对象,提出一类基于数据驱动的控制器设计及其参数整定方法.方法首先依据非参数时变动态线性化定理提出3种控制器结构,再采用迭代反馈整定方法(IFT)优化其控制器参数,从根本上解决了IFT方法给定控制器结构时存在的盲目性.最后将该方法与另外两种数据驱动控制方法---无模型自适应控制(MFAC)和IFT方法进行比较研究,结果表明方法是有效的.     

统计能量分析中参数不确定性分析

统计能量分析方法是计算结构高频振动噪声的有效方法之一，内损耗因子和耦合损耗因子是其中重要的参数但不易测量，测量误差通常比较大，导致计算得到的子系统振动能量和真实值之间存在偏差.为解决上述问题，该文采用了4种不同的区间分析方法:区间矩阵摄动法、基于区间变量特性法、仿射算法和仿射逆矩阵法，从理论上计算了统计能量分析子系统的振动能量区间，该区间结果充分考虑了内损耗因子和耦合损耗因子的测量误差对计算结果的影响，对传统的统计能量分析理论进行了完善.然后，通过算例比较了每种方法所求子系统总能量区间的优劣.     

多星测控调度效能评价指标体系研究

分析了建立多星测控调度问题评价指标体系的工程需求.从测控网管理方的角度,定义了反映测控系统服务能力、利用效率和资源配置合理性的指标;针对航天器拥有方的需求,建立了反映接受测控服务情况和反映航天任务满足程度的指标.通过两大部分指标构建了多星测控调度问题的指标体系.通过算例说明了利用该指标体系进行多星测控系统效能分析的可行性.     

有色噪声激励下双稳态电磁式振动能量捕获器动力学特性研究

随着微机电科技的进步,利用环境振动进行系统自供电已经成为目前非线性动力学研究的热点.以附加线性振子的双稳态电磁式振动能量捕获器为研究对象,建立系统的动力学方程,通过数值仿真研究了有色噪声激励作用下双稳态能量捕获系统的动力学行为,分别从有色噪声强度、质量比和调频比3个方面研究了双稳态系统动力学响应,获得了上述参数对双稳态能量捕获系统动力学特性的影响规律,上述研究结果为双稳态电磁式振动能量捕获系统的相关研究提供理论基础.     

基于非线性能量阱的双频激励非线性系统减振

针对某型民用航空发动机双频带激励特点,建立了单自由度线性振子耦合非线性能量阱（nonlinear energy sink,NES）的动力学模型.根据典型双转子发动机在巡航状态下低、高特征频率比（1∶4.74）,为系统设定双频带简谐外激励.利用四阶Runge-Kutta算法,研究了耦合NES振子时系统的振动抑制特征,并从外激励频率对系统主振子动能、系统总体能量的影响等方面,与未耦合NES系统、耦合线性动力吸振器两种情况下的数值计算结果进行对比分析.研究结果表明NES对双频带外激励具有更好的振动抑制效果,用NES降低航空发动机振动有可行性.     

A study on torsional vibration attenuation in automotive drivetrains using absorbers with smooth and non-smooth nonlinearities

The automotive industry is predominantly driven by legislations on stringent emissions. This has led to the introduction of downsized engines, incorporating turbocharging to maintain output power. As downsized engines have higher combustion pressures, the resulting torsional oscillations (engine order vibrations) are of broadband nature with an increasing severity, which affect noise and vibration response of the drive train system. Palliative devices, such as clutch pre-dampers and dual mass flywheel have been used to mitigate the effect of transmitted engine torsional oscillations. Nevertheless, the effectiveness of these palliative measures is confined to a narrow band of response frequencies. The nonlinear targeted energy transfer is a promising approach to study vibration mitigation within a broader range of frequencies, using nonlinear vibration absorbers (or nonlinear energy sinks – NESs). These devices would either redistribute vibration energy within the modal space of the primary structure, thus dissipating the vibrational energy more efficiently through structural damping, or passively absorb and locally dissipate a part of this energy (in a nearly irreversible manner) from the primary structure. The absence of a linear resonance frequency of an NES, enables its broadband operation (in contrast to the narrowband operation of current linear tuned mass dampers). Parametric studies are reported to determine the effectiveness of various smooth or non-smooth nonlinear stiffness characteristics of such absorbers. A reduced drivetrain model, incorporating single and multiple absorber attachments is used and comparison of the predictions to numerical integrations proves its efficacy.     

Application of non-smooth NES in vibration suppression of rotor-blade systems

The non-smooth nonlinear energy sink (NSNES) is used to suppress the vibration of the rotor-blade system. Firstly, the structure and working principle of the NSNES for rotor-blade system are introduced. Then, the dynamics model of the rotor-blade-NSNES system is established by Lagrangian method. And then, numerical simulations are applied to evaluate the vibration suppression ability of the NSNES on rotor and blade. The results show that the suppression rates of NSNES on the rotor and the blade can reach 81% and 74% in steady state resonance under given parameters, respectively; and for transient vibration of blade, a 1.85 times dissipating speed is obtained in rotor-blade system with NSNES than that without NSNES. In particular, NSNES has better vibration suppression capability than linear dynamic vibration absorber (LDVA) when both have the same vibration absorption mass.     

Reduced-order model for laminar vortex-induced vibration of a rigid circular cylinder with an internal nonlinear absorber

The nonlinear interaction of a laminar flow and a sprung rigid circular cylinder results in vortex-induced vibration (VIV) of the cylinder. Passive suppression of the VIV by attaching an internal nonlinear vibration absorber that acts, in essence, as a nonlinear energy sink (NES) to the cylinder has been observed in finite-element computations involving thousands of degrees of freedom (DOF). A single-DOF self-excited oscillator is developed to approximate the limit-cycle oscillation (LCO) of the cylinder undergoing VIV. This self-excited oscillator models the interaction of the flow and the cylinder. Then, a two-DOF reduced-order model for the system with the internal NES is constructed by coupling the single-DOF NES to the single-DOF self-excited oscillator. Hence, the complicated high-dimensional system of flow-cylinder-NES involving thousands of DOF is reduced to a two-DOF model. The two targeted energy transfer mechanisms responsible for passive VIV suppression that are observed in the finite-element computations are fully reproduced using the two-DOF reduced-order model. This reduction of the dynamics to an easily tractable low-dimensional reduced-order model facilitates the approximate analysis of the underlying dynamics. Moreover, the underlying assumptions of the order reduction, and the parameter ranges of validity of the reduced-order model are formulated and systematically studied.     

Multi-mode model of a piezomagnetoelastic energy harvester under random excitation

Abstract: The transformation of ambient vibrational energy into electric energy through the use of piezoelectric energy harvesting devices has been the subject of numerous investigations [1]. A commonly studied energy harvesting device performing especially well under broadband excitation, is the piezomagnetoelastic energy harvester investigated by Erturk et al. [2], which is usually discretised for the fundamental vibration mode resulting in a single-mode model. This contribution presents the study of a multi-mode model of the piezomagnetoelastic energy harvester under random excitation. The probabilty density function (PDF) is computed to be the solution of the corresponding Fokker-Planck equation using a Galerkin type method [3,4]. Based on the PDF, the resulting voltage variance is computed as a measurement for the expected power output as demonstrated in [5]. The results of the multi-mode model are then compared with the results of the single-mode model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of Periodic Solutions of a Third-Order Nonlinear System

Differential Equations - We consider a nonlinear autonomous third-order ODE system depending on numerical parameters and describing the motions of an energy harvester that converts residual thermal...     

Modeling the capacity of a novel flow-energy harvester

The performance of a new type of flow energy harvester based on oscillating foils is investigated through numerical modeling by using two methods, a 2D thin-plate model and a 3D nonlinear boundary-element model. The fluid–structure interaction problem involved in the dynamics of a heaving/pitching foil coupled with an actuation/energy harvesting system in this device is examined. The 2D analysis allows us to simulate dynamics of the flapping-foil system over a large range of parameters and to identify areas of special interests (e.g., high energy output or high efficiency). In the vicinity of these areas the 3D model can accurately predict the performance of the system. By examining the power extraction capacity and efficiency of the system at various geometric, mechanical, and kinematic parameters, the optimal performance of the system is determined. In addition, the performance is found to be enhanced by the presence of a solid ground, as well as the thickness of the foil (at certain frequencies).     

Modelling and passive control of flexible guiding hoisting system with time-varying length

ABSTRACT

A coupled dynamic modelling of the flexible guiding hoisting system is established, which includes the transverse-longitudinal-coupled vibration and the rotational vibration. Substituting vibrational energy of the system into Hamilton principle and applying the dynamic constraint, a distributed parameter mathematical model of the multi-rope system is derived. It is governed by coupled partial differential equations and ordinary differential equations (PDEs-ODEs), where the dynamic constraint in the form of an unknown moving force is the only connection between the hoisting conveyance and the guiding ropes. Based on Galerkin method, the dynamic response of the system is validated by numerical calculation and ADAMS simulation. Besides, an absorber with artificial intelligence optimization is proposed to reduce system vibration. The simulation result has demonstrated that a hoisting conveyance resonance can be observed when the external disturbance frequency is close to the system natural frequencies. Moreover, a vibration absorber can effectively diminish the resonant peaks of the first three orders of the guiding rope.