Finite element formulation for dynamics of planar flexible multi-beam system

In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation. Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution using the present coupling finite element formulation.     

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact

Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted flexible beam is investigated. The Hertzian contact law is used to describe the impact process, and the dynamic equations are formulated in the floating frame of reference using the assumed mode method. The two important geometric nonlinear effects of the flexible beam are taken into account, i.e., the longitudinal foreshortening effect due to the transverse deformation, and the stress stiffness effect due to the axial force. The simulation results show that good consistency can be obtained with the nonlinear finite element program ABAQUS/Explicit if proper geometric nonlinearities are included in the floating frame formulation. Specifically, only the foreshortening effect should be considered in a pure transverse impact for efficiency, while the stress stiffness effect should be further considered in an oblique case with much more computational effort. It also implies that the geometric nonlinear effects should be considered properly in the impact dynamic analysis of more general flexible multibody systems.     

Stabilization of geometrically nonlinear topology optimization by the Levenberg–Marquardt method

This paper deals with the design of compliant mechanisms in a continuum-based finite-element representation. Because the displacements of mechanisms are intrinsically large, the geometric nonlinearity is essential for designing such mechanisms. However, the consideration of the geometric nonlinearity may cause some instability in topology optimization. The problem is in the analysis part but not in the optimization part. To alleviate the analysis problem and eventually stabilize the optimization process, this paper proposes to apply the Levenberg–Marquardt method to the nonlinear analysis of compliant mechanisms.     

Stability analysis of a class of digital filters utilizing single saturation nonlinearity

A novel criterion for the global asymptotic stability of a class of digital filters utilizing single saturation nonlinearity is presented. An example showing the effectiveness of the present criterion is given.     

GaN压电半导体杆的非线性动态响应研究

利用有限元分析方法,研究了p型GaN压电半导体杆在简谐力作用下的拉伸振动问题,得到了位移、电势和空穴浓度非线性动态响应的数值解,并分析了简谐力对p型GaN压电半导体杆力电耦合性能的调控作用。研究结果表明,简谐力显著地影响压电半导体杆内力电场的分布情况:由于电流密度中的电非线性项,电场和空穴浓度的分布失去对称性或反对称性;力电场在简谐力驱动下表现为周期性变化,但空穴浓度的动态响应表现为明显的非对称波动。     

5G光载无线通信前传系统数字预失真线性化研究

第五代移动通信系统新空口(5G NR)的信号带宽、调制度和峰均比相比4G信号高很多。用于小蜂窝或微蜂窝基站组网的光载无线通信(Radio-over-Fiber, RoF)前传系统的非线性失真也更加严重。为了使5G NR信号线性传输,采用记忆多项式(Memory Polynomial, MP)和广义记忆多项式(Generalized Memory Polynomial, GMP)模型构建数字预失真器,矫正5G RoF前传系统的非线性。在实验中搭建了2 km光纤的RoF前传系统,并采用100 MHz带宽5G NR信号作为测试信号对其进行线性化测试。实验结果表明,采用MP和GMP数字预失真器进行线性化时,5G RoF前传系统的邻信道功率比(Adjacent Channel Power Ratio, ACPR)可分别改善13 dB和17 dB以上。这说明MP和GMP数字预失真器对5G RoF前传系统的非线性具有显著的抑制作用。因此基于MP和GMP两个模型的数字预失真器均可用于5G RoF前传系统的线性化,而且GMP预失真器比MP预失真器对该系统线性化的能力更强。     

周期激励下广义离散Duffing系统的多稳态分析

具有硬边界的动基座双自由度动力学系统在受到基座周期性激励与随机冲击扰动时,振子与边界碰撞后的强非线性特性导致系统产生复杂的混沌行为.本文基于Soft Actor-Critic强化学习框架,构建了同时实现振动控制与基座运动跟随的智能算法,研究了宽频域范围内含有硬边界约束的动基座双自由度系统的动力学控制效果.通过构建包含相对位移、控制力的复合奖励函数,实现动力学系统精度较高的轨迹跟踪与振动抑制.结果表明,该算法可以实现频率范围跨2个数量级(0.01Hz到1Hz)的有效振动控制,并通过与PID控制方法的比较,展现了该方法在复杂环境中的稳定性与泛化性.     

Quantification of different effects occurring during fatigue tests on bituminous mixtures

Quantification of different effects (nonlinearity, heating, thixotropy, and fatigue) occurring during fatigue tests on bituminous mixtures is presented in this paper. A focus is given on the nonlinearity phenomenon. Continuous fatigue tests and a test with specific protocol (called fatigue tests to estimate biasing effects) were performed in tension/compression mode on cylindrical samples of the same material. The analysis of results reveals that reversible effects (nonlinearity, heating, and thixotropy) are important (more than 90% decrease at 100,000 cycles for a strain amplitude of 100 μm/m at 10 Hz) and cannot be ignored when interpreting classical fatigue tests. The nonlinearity effects respect the time‐temperature superposition principle, and they are more pronounced at “high” temperature (at the same frequency). Direction of nonlinearity curve in the Cole‐Cole axes is shown to be independent of temperature and frequency for the considered range.     

基于LS-SVM的不确定非线性系统滑模控制

针对滑模控制中不确定上界值的问题,提出了一种基于LSSVM自适应上界学习的滑模控制方法.首先将系统分为确定部分和不确定部分,对确定部分采用状态反馈法进行控制,对不确定系统部分采用最小二乘支持向量机( LSSVM)来完成.该控制器不仅可以保证非线性不确定系统渐近稳定,降低一般滑模控制理论分析的条件,还有效地抑制了抖振.仿...     

On the lower bounds of the second order nonlinearities of some Boolean functions

The rth order nonlinearity of a Boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers. It is also important in coding theory as it is related to the covering radius of the Reed-Muller code R(r,n). In this paper we deduce the lower bounds of the second order nonlinearities of the following two types of Boolean functions:

1.

with d=2^2r+2^r+1 and , where n=6r.

2.

, where x,y∈F_2^t,n=2t,n?6 and i is an integer such that 1?i<t,gcd(2^t-1,2ⁱ+1)=1.

For some λ, the functions of the first type are bent functions, whereas Boolean functions of the second type are all bent functions, i.e., they possess the maximum first order nonlinearity. It is demonstrated that in some cases our bounds are better than the previously obtained bounds.